MPTET Varg 1 Physics Mock Test - 2 - MPTET MCQ

दिए गए विकल्पों में से "भर्ता" शब्द 'पति' का पर्यायवाची है।
पति के अन्य पर्यायवाची शब्द - स्वामी, प्राणाधार, प्राणप्रिय, प्राणेश, आर्यपुत्र, दूल्हा, वल्लभ, भर्तार, सुहाग, सौहर, साजन, बालम, वर।
स्पष्टीकरण
अन्य विकल्प:

• विधाता के पर्यायवाची शब्द - ब्रह्मा, विधि, सृष्टिकर्त्ता।
• विभु के पर्यायवाची शब्द - सर्वव्यापक, नित्य, अनन्त, अजन्मा।
• भार्या के पर्यायवाची शब्द - प्रिया , अंगना , पत्नी , प्रणयिनी , प्रेमिका , स्त्री , वामा।

अन्यसंबंधित बिंदु
पर्यायवाची शब्द:
सामान्य अर्थ में ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।
पर्यायवाची शब्द के कुछ उदाहरण :

• अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
• इज्जत– मान, प्रतिष्ठा, आदर, आबरू।
• उपहास– परिहास, मजाक, खिल्ली।
• एकांत – निर्जन सुनसान शून्य।
• औषधि- दवा, दवाई, भेषज।
• किरण- अंशु, रश्मि, कला, कर, गो, प्रभा, दीधिति, मयूख, मरीचि।
• कंठ- गला, शिरोधरा, ग्रीवा, गर्दन।
• गाय- भद्रा, गौरी, सुरभी, धेनु, गऊ, गौ,गैया, पयसि्वनी,दोग्धी।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
• झंडा- पताका, केतु, निसान, ध्वज, केतन, वैजयंती।

'उत्तराधिकार में प्राप्त सम्पत्ति - इन अनेक शब्दों के लिए एक शब्द है- 'रिक्थ'
गलतीअंक

• वह गुण, वस्तु या विचार जो परम्परा के रूप में हमें पूर्वजों से मिला हो - धरोहर
• किसी की मृत्यु के बाद उसकी सम्पत्ति पाने का अधिकार - उत्तराधिकृत
• वह मूल्यवान वस्तु जिस पर किसी का अधिकार हो - परिसम्पत्ति

स्पष्टीकरण

• अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्यसंबंधित बिंदु
कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द:-

• जिस पर मुकदमा चल रहा हो - अभियुक्त
• किसी एक में ही आस्था रखने वाला - अनन्य
• वह चीज जिसकी चाहत हो - इच्छित
• जिसके ऊपर किसी का उपकार हो - उपकृत
• जो इन्द्रियों से संबंधित हो - ऐन्द्रिय
• जिसकी बुद्धि बहुत तेज हो - कुशाग्र
• जिसका कुछ ही समय में नाश हो जाए - क्षणभंगुर
• जो दूसरों में केवल दोषों को ही खोजता हो - छिद्रान्वेषी

सही उत्तर है - कृपा करना, दया करना, मानसिक पीड़ा, शारीरिक रोग
स्पष्टीकरण

• अनुग्रह -कृपा; प्रसाद। ईश्वरीय कृपा। राज्य की कृपा से प्राप्त सहायता या सुविधा।
• आधि- अभाव जनित रोग, मानसिक स्थिति की नकारात्मक छवि। व्याधि- शारिरिक कष्ट, वात, पित्त, और कफ की स्थिति।

महत्वपूर्णबिंदु

• भिन्नार्थक शब्द: जो शब्द सुनने में एक जैसे लगते हैं लेकिन उनका अर्थ अलग होता है उन्हें भिन्नार्थक शब्द कहते हैं।
• इन्हे श्रुतिसम भिन्नार्थक या शब्द युग्म भी कहते हैं।

अन्यसंबंधित बिंदु
पर्यायवाची शब्द

• जो शब्द समान अर्थ के कारण किसी दूसरे शब्द की जगह ले लेते हैं उन्हें पर्यायवाची शब्द कहते हैं
• या समान अर्थ प्रदान करने वाले शब्द पर्यायवाची शब्द अथवा समानार्थक शब्द कहलाते हैं।

समानार्थी

• समानार्थी का अर्थ होता हैं (सामान + अर्थ) अर्थात किसी शब्द का सामान अर्थ वाले दूसरे शब्द या उसी के सामान कोई दूसरा नाम (वस्तु)।
• “वे शब्द जिनका अर्थ एक समान होता हैं समानार्थी शब्द कहलाते हैं समानार्थी शब्द को हम पर्यायवाची शब्द भी कहते है।

The correct answer is 'woe'.

Explanation

• Jubilation: A feeling of great happiness, especially because of a success
  • ​E.g.- The news was greeted with jubilation.
• Woe: A strong feeling of sadness
  • ​​E.g.- The city's traffic woes are well-known.

Hence, the correct answer is 'woe'.

Other Related Points

• Happiness: The feeling of being happy
  • ​​E.g.- It was only later in life that she found happiness and peace of mind.
• Festivity: The parties, meals, and other social activities with which people celebrate a special occasion
  • ​​E.g.- Come in and join the festivities!​
• ​Triumph: A great success or victory; the feeling of happiness that you have because of this
  • ​​​E.g.- The team returned home in triumph.

Bhakra Nangal Project is the biggest multipurpose river valley project in India.

Explanation

• The Bhakra Nangal Dam is a concrete gravity dam in India.
• It is located near the border between Punjab and Himachal Pradesh in the northern part of the country.
• Situated across the Sutlej River, this dam is said to be the second-tallest dam in Asia, with a height of 740 ft.
• It is the biggest multipurpose river valley project in India.
• One of the primary uses of this dam is storing rainwater for irrigation purposes.
• The water of the dam helps in providing electricity to many areas of the states of Himachal Pradesh, Chandigarh, Haryana, Rajasthan, Punjab, and Delhi.
• It is a popular tourist destination that was called the ‘New Temple of Resurgent India’ by the country’s first prime minister, Jawaharlal Nehru.

• The reservoir of this dam is called the ‘Gobind Sagar’.

Piaget and Vygotsky proposed theory regarding the role of language for development and the relationship between language and thought.

• According to Piaget, thought comes before language, which is only one of its forms of expression. The formation of thought basically depends on the coordination of sensory-motor schemes and not of language. This can occur only after the child has reached a certain level of mental abilities, subordinating herself, to the thought processes. The language allows the child to evoke an object or event absent at the communication of concepts.
• Piaget insists that the language and thought of the child are aspects of cognitive processes. The intellectual development of the child can be understood through his/her language and thought processes.
• Piaget primarily concentrated on the cognitive aspect, another dimension was added by Vygotsky
• According to Vygotsky, thought and language is interdependent processes, from the beginning of life. The acquisition of language by the child modifies its higher mental functions: it gives a definite shape to thought, enables the emergence of imagination, memory usage, and action planning.
• All fundamental cognitive activities including language take place in a matrix of social history. He believed that cognitive skills and patterns of thinking are not determined by innate factors but are the product of the interaction between the individual and the socio-cultural institution where the individual grows up.

Hence, from the above point it is clear that according to Piaget, a thought emerges first and according to Vygotsky, language has a profound effect on thought.

A school curriculum is a complete set of organized experiences in the school. It includes aims, objectives, teaching content, teaching strategies, and all teaching-learning aids to cater totality of student's experiences that occur in the educational process.

Explanation

The sequential order of curriculum development:

• Assessment of needs: In this process, the teacher assesses students regularly to check and report on their progress and make decisions about further teaching. Therefore it is important that a teacher adopts a responsible and sensitive approach towards assessment.

• Formulation of objectives: After assessing the needs or requirement area, the next of developing a curriculum is to formulate the objectives as per the student's learning needs. Those objectives should be formulated which would be achieved at the end of the course.

• Selection of texts/learning experiences: Selection of learning resources is a very important and crucial step for developing a curriculum. The learning resources should be as per the needs and desires of the learning. It should be complementary in achieving formulated learning objectives. It should give direct experience to the learner and makes the learning more effective.

• Evaluation of the curriculum: Evaluation procedures to be done to check the results of the curriculum after the implementation. Through this, the school administration will get the optimum feedback on what should be added and what should be removed from the curriculum to make it more significant.

Other Related Points

Salient features of curriculum:

• Makes learning an integrated process.
• Nurtures learner's holistic development.
• Introduces structure of program of study.
• Improves totality of student's experience.
• Includes teaching strategies and contents.
• Promotes inclusive education to all learners.
• Provides ample opportunities for all-round development.

Hence, it could be concluded that assessment of needs, formulation of objectives, selection of texts/learning experiences, evaluation is the sequential order of curriculum development.

Learning Disability is a neurological disorder that affects the way one receives and processes information. There are various types of learning disabilities in children.

Explanation

• Dyspraxia is a developmental disorder of the brain in childhood causing difficulty in muscle control as well as activities requiring coordination and movement.
• This motor skill development is a type of learning disability specifically related to motor skills.
• It is also known as developmental coordination disorder or motor learning disability.
• Children with dyspraxia struggle with coordination and movement.

Hence, it can be inferred that a disorder characterized by problems with movement and motor skill coordination is Dyspraxia.

Concept:

For a translational motion force causes the particle to accelerate in a straight line and similar to this for rotational motion the coupled forces (equal and opposite forces) causes any particle to rotate along some axis of rotation as shown below and this coupled force is known as Torque or Moment of force.

Thus, torque is a type of force that can cause an object to rotate along some axis of rotation.

And it can be given as

Torque,

⇒

Here τ is the torque acting on an object whereas r is the distance between forces or axis of rotation and θ is angel between r and F

Application:

• If the doors are provided with handles near the outer edges away from the hinges the force or the distance between the axes of rotation will increase.
• As the distance value increased, the torque also increased, so to apply maximum torque to the door.
• Hence, doors are provided with handles near the outer edges for easy opening.

Concept:

• Pascal is a unit of pressure which is defined as the force per unit area.
• The formula for the coefficient of the viscosity, , where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity
• The time can be written in terms of velocity and distance as,

Explanation:

Pascal is a unit of pressure which is defined as the force per unit area.

The SI unit of pressure-Time is . . . . . . . . .(1)

The formula for the coefficient of the viscosity,

where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity

The SI unit of the coefficient of the viscosity is . . . . . . . . (2)

where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity

From equation (1) and equation (2), we can conclude,

the dimension formula of the pascal-second is equal to the dimensional formula of the coefficient of viscosity.

Other Related Points

• The dimensional formula of the force,
• The dimensional formula of the energy,
• The dimensioal formula of the pressure,

CONCEPT:
The potential difference across the capacitor is written as;

V_rms is the potential difference in root mean square.
CALCULATION:
Given: V_rms = 220 V
As we know,

⇒
Hence, option (4) is the correct answer.

The correct answer is the Height of the liquid column present in the vessel.
Concept:
According to Pascal’s Law,

• the pressure or intensity of pressure at a point in a static fluid is equal in all directions. fluid pressure is always perpendicular to the wall of the container
• This law is valid for the cases of fluid flow where shear stresses do not exist. The cases are
• Fluid at rest
• No relative motion exists between different fluid layers. For example, fluid at a constant linear acceleration in a container.
• Ideal fluid flow where viscous force is negligible.
  

Hydrostatic Law:

• states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point.
• If P0 is the atmospheric pressure for a point at depth h below the surface of a liquid of density p.
• Hydrostatic pressure(P) = Po + ρ × g × h​

Hydrostatic pressure depends on the followings:

• Depth of the point below the surface (h)
• Nature of the liquid (ρ)
• Acceleration due to gravity (g)

Hydrostatic pressure is independent of the followings:

• Amount of liquid
• The shape of the container
• The cross-sectional area.

Important Points
Applications of Pascal's law:

1. Centrifuge: Centrifugation is used to separate the contents of mixtures according to their size and density. The centrifuge works on the principle of sedimentation.
2. Hydraulic Lift: The lift that uses pascal's law and is used to lift objects with the help of fluid is called hydraulic lift. It works on Pascal's law.
3. ​Motor: A motor is an electrical device that converts electrical energy into mechanical energy. It works on the principle that a current-carrying conductor experiences a mechanical force when it is placed in a magnetic field.

• Lever: A lever is a simple machine that is made up of two load arms and a fulcrum. The distance from the fulcrum can be used to determine how the input and output forces are related to each other.

The correct answer is option 1) i.e. Each point in a wavefront is a source of secondary waves.
Concept:
Huygens' concepts of secondary wavelets:

• Huygen’s principle states that every point on the wavefront may be considered as a source of secondary spherical wavelets that spread out in the forward direction at the speed of light.
  • The new wavefront is the tangential surface of all these secondary wavelets.
  • Secondary sources start making their own wavelets, these waves are similar to that of the primary source
  • It states that each point on a wavefront is a source of wavelets, which spread forward with the same speed.

• Wavefront: A wavefront is a surface or a line on which the disturbance at every point has the same phase.
• Wavelets: It is a wave-like oscillation with an amplitude that starts at zero, increases, and then decreases back to zero.

Explanation:

• Huygens's principle states that each point on a wavefront is a source of wavelets, which spread forward with the same speed.

Concept:-
Force:-

• Force is an external cause that is capable of changing the state of rest or motion of a particular object.
• Force is a vector quantity. So it has both magnitude and direction.
• The direction along which a force is applied is known as the direction of the force and the point where force is applied is called the application point.
• Usually, the magnitude of Force is measured by using a spring balance.
• The SI unit of force is Newton (N).
• The physical quantity force is quantified by the product of mass (m) with acceleration (a).
• The force can mathematically be expressed as:-

F = ma
Where,
m = mass
a = acceleration
It is articulated in Newton (N) or Kg m/s2.
Calculation:-
The parallelogram law:-

• When two vectors are acting simultaneously at a point, then it can be represented both in magnitude and direction by the adjacent sides drawn from a point.
• So, the resultant vector is completely represented both in direction and magnitude by the diagonal of the parallelogram passing through the point.

Let R be the resultant of two vectors P and Q.
According to the parallelogram law of vector addition, the resultant R is the diagonal of the parallelogram of which P and Q are the adjacent sides as shown in the figure.

The magnitude of R is given by

where, θ is the angle between P and Q.
Similarly, if we consider P as F₁ and Q as F₂ then the diagonal will be vector F₃.

Concept:

• If a wire is under force, there will be an increase or decrease in length due to the developed stress and strain in it.
  • Normal Stress is calculated by perpendicular Force (F) divided by the cross-section area (A) on which it is applied.

Normal Stress = F/A

• The strain is the change in length of wire (l) divided by the original length (L) of the wire.
  Strain = l/L
• Hook's Law of elasticity Young's modulus = stress/strain

Explanation:
​Given diagram as said in the question:

For the given diagram:
Stress = F/A
Strain = l/L
We know from Hook's law that




So the force required to increase the length of the wire by 'l' is:

Hence the correct answer is option 1.

Concept:

• Equilibrium: It is a state of a body in which overall change in a body is zero.
• Translational Equilibrium: A body is said to be in translational equilibrium if the net sum of all the forces (F) acting on a body is zero.

ΣF = 0
F_net = 0
F₁ + F₂ + F₃ + ............... + F_n = 0

• Rotational Equilibrium: A body is said to be in rotational equilibrium if the net sum of all the torque (τ) acting on a body is zero.

Σ τ = 0
τ_net = 0
τ₁ + τ₂ + τ₃ + .................. + τ_n = 0
Calculation:

• First, draw the FBD of the given figure and resolve it into a horizontal and vertical component
  ​
• Horizontal component

T₁ Cos 30° = 100 Cos 60°
T₁ = 100 / √3 N

• Vertical Component

T₁ Sin 30° + 100 Sin 60° = W
By putting the value of T₁ from above we get
= W
W = 200 / √3 N
Hence option 3 is correct.
Other Related Points

• Solving the numerical problem on the equilibrium of forces always draws the FBD (Fee Body Diagram).
• A simplified version of the body on which all external forces are shown is called FBD (Fee Body Diagram) of the given body.

Reversible Processes:

• A thermodynamic process driving from initial state to final state is said to be reversible, if the system as well as its surrounding returns back to its initial state, without any change in the universe.
• The processes which can be idealized as reversible are Motion without friction, Expansion/ compression with infinitesimal pressure difference, Energy transfer as heat with infinitesimal temperature difference, isothermal and adiabatic.

Irreversible Processes:

• A thermodynamic process that does not return back to its initial state is termed as an irreversible process.
• The examples of irreversible processes are Motion with friction, Throttling, Free expansion, Constant Volume and constant pressure, Expansion/ compression with finite pressure difference, Energy transfer as heat with finite, mixing of matter at different states, Mixing of non-identical gases.

Concept:

• Projectile motion: A kind of motion that is experienced by an object when it is projected near the Earth's surface and it moves along a curved path under the action of gravitational force.
• When a particle moves in projectile motion, its velocity has two components.
  1. ​​vertical component (u sinθ)
  2. horizontal component (u cosθ)

• The time of flight of projectile is given by

where u is the velocity, makes an angle 'θ' with the x-axis, and g is the gravitational acceleration.

• The range of flight is given by

where u is the velocity, makes an angle 'θ' with the x-axis, and g is the gravitational acceleration.

• The maximum height a projectile can attain

Calculation:
Let us consider the initial velocity of the projectile is u m/s, H is the maximum height of the projectile and R is its horizontal range.

• The time of flight of projectile is given by

where u is the velocity, makes an angle 'θ' with the x-axis, and g is the gravitational acceleration.

• The maximum height a projectile can attain

H = nT2

Concept:

• Angular Momentum (L): It is a property of a body in rotational motion.
  • The moment of linear momentum is known as angular momentum.

L = r × p = r × mv
where p is the momentum of the body, r is the distance of linear momentum from the axis of rotation, m is the mass of the body, and v is the velocity of the body.

• Linear momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.
• Angular momentum Conservation: When in a system, there is no external torque then the total angular momentum (L) of the system will be conserved.

Explanation:

• If net external torque on a rotating object is zero, Its angular momentum will be conserved i.e. will be constant.
• Linear momentum is conserved when there is no external force on the body.
• Linear velocity is constant when a body is moving with a constant speed and constant direction.
• The angular velocity of a body is constant if it is moving in a uniform circular motion.
• So the correct answer is option 4.

Concept:

As per radioactive decay law, the total number of nuclei of radioactive compounds after radioactive decay in the sample is given by given equation

where N is the number of nuclei of radioactive compounds after radioactive decay, N0 is the number of nuclei of radioactive compounds initially, λ is the decay constant and t is the time of radioactive decay.

The half-life of a radioactive element (T1/2): The time interval in which the mass of a radioactive substance or the number of atoms reduced to half of its initial value.

The expression for the half-life is

Where λ = is the decay rate constant

Calculation:

Given - T = 90 days, t = 30 days

The number of half-lives (n) in 90 days is:

As we know:

Concept:

For two vectors and , the resultant will be:

Calculation:

Given:

cos θ = -1/2

Concept:

• Electric field (E): The region around an electric charge in which other charge particles experience an attractive or repulsive force is called an electric field.

Electric field (E) =

• Unit of E will be N/C.
• Electric potential: The amount of work done in moving a unit charge from a reference point to a specific point in the electric field without producing any acceleration is called electric potential.
  • Volt (V) is the SI unit of the Electric Potential.

The relation between an electric field and an electric potential is given by:
E = Potential (V)/distance (r)

• Unit of E will be Volt/meter.

Energy (E) = charge (q) × Potential difference (V)
Volt = J/C
Unit of E = J/Cm
Explanation:
Since E = V/r
The SI unit of E = SI unit of V/ SI unit of r = Volt/meter = V/m

• The SI unit of the electric field (E) = V/m

Energy (E) = charge (q) × Potential difference (V)
Volt = J/C

• Unit of E = J/Cm
• Unit of E will be N/C.
• The J/C is not the unit of the electric field. Hence option 3 is correct.

CONCEPT.

• Lorentz force: It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force on the charged particle is called the Lorentz force and is given by

​⇒ FL = qE + qvBsinθ

• A charged particle experiences a force when it moves in a magnetic field.

​⇒ F = qvBsinθ

Where, F = force due to magnetic field, q = magnitude of charge, v = velocity of charge, B = magnetic field and θ = angle between v and B​

EXPLANATION:

• We know that a charged particle experiences a force when it moves in a magnetic field.
• The force experienced by a charged particle when it moves in a magnetic field is given as,

​⇒ F = qvBsinθ -----(1)

Where, F = force due to magnetic field, q = magnitude of charge, v = velocity of charge, B = magnetic field and θ = angle between v and B

• By equation 1 it is clear that if q, v, and B are constant, then the force depends on the angle between v and B.
• We know that sinθ is maximum when θ = 90°.
• So we can say that the magnetic force on the electron will be maximum when it is moving perpendicular to the magnetic field. Hence, option 2 is correct.

Concept:

• The first law of thermodynamics states that energy can neither be created nor be destroyed but it can be transformed from one state to another.
  • From the first law, ΔQ = ΔU + ΔW; where ΔQ is the heat supplied to the system, ΔU is the corresponding change in its internal energy, and ΔW is the work done by the system.

Explanation: ​

• An isochoric process in the context of thermodynamics is a term used to describe a situation where the volume of a system remains constant.
• According to the question, the work done by the system equals zero.
  • ​Work done is given by, ΔW = PΔV
  • If the volume of the system remains constant then ΔV = 0 ⇒ ΔW = 0
  • The process will be Isochoric.​

Other Related Points

• In the isothermal process, the temperature of the system remains constant which means ΔT = 0.
• In the isobaric process, the pressure of the system remains constant which means ΔP = 0.
• In the adiabatic process, there is no heat exchange between the system & surroundings which means ΔQ = 0.

Law of Parallelogram of forces:
This law is used to determine the resultant of two coplanar forces acting at a point.
It states that “If two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through that common point.”

Let two forces F₁ and F₂, acting at the point O be represented, in magnitude and direction, by the directed line OA and OB inclined at an angle θ with each other.
Then if the parallelogram OACB be completed, the resultant force R will be represented by the diagonal OC.

Calculation:
F₁ = 3 kN, F₂ = 4 kN, θ = 60°
F_R = (3² + 4² + 2 × 3 × 4 cos 60)^1/2
F_R = 6.08 kN

CONCEPT:

Velocity:

• The rate of change of displacement of an object (displacement over elapsed time) is velocity.
• Velocity is given by,

Acceleration:

• The rate of change of velocity is acceleration.
• Like velocity, acceleration is a vector and has both magnitude and direction.
• Acceleration is given by,

​

CALCULATION:

Given:

The position of a particle as a function of time t (i.e., displacement) is x = t³- 2t² + 2

• Now the velocity will be,

Now at t = 4sec,

The velocity will be,

⇒ v = 3 × 4² - 4 × 4 = 48 - 16 = 32 m/s

⇒ v = 32 m/s

Concept:

• Average velocity is calculated by dividing your displacement (a vector pointing from your initial position to your final position) by the total time.
• Average speed is calculated by dividing the total distance you traveled by the total time.
  • 

Calculation:

Given: x(t) = αt + βt3 ;where α = 2.0 m/s, β = 0.01 m/s3

x_f = x_(t=4) = 2 × 4 + 0.01 × 4³

x_(t=4) = 8.64

Similarly,

x_i = x_(t=2) = 2 × 2 + 0.01 × 23

x_(t=2) = 4.08

Therefore,

This is the required velocity.

Concept:
Electrostatic External Field Torque- It is defined as the product of the moment and field and it is written as;
Electrostatic External Field Energy - It is defined as the dot product of moment and the field is written as;
Calculation:
As we know;
Electrostatic External Field Torque- It is defined as the product of the moment and field and it is written as;
​​
Electrostatic External Field Energy - It is defined as the dot product of moment and the field is written as;

The electrostatic axial field for a short dipole - The Electrostatic axial field for a short dipole is written as;

Electrostatic Equatorial Field for a short Dipole is written as;

Hence option (1) is the correct answer.

CONCEPT:

The potential of the given conduction sphere is written as;

V =

⇒ V = k

Here V is the potential, Q is the charge, and k is the constant of proportionality.

CALCULATION:

According to the potential of the condition sphere we have;

V = k

Where R is inversely proportional to the applied potential.

In this question, we have two hollow conducting spheres where R₁ >> R₂. The larger the radius the smaller the potential for the given conducting spheres.

So, R₂ is having large potential than R₁.

Hence, option 3) is the correct answer.

Concept:
Solenoid:

• The solenoid consists of a long wire wound in the form of a helix where the neighbouring turns are closely spaced, so each turn can be regarded as a circular loop.
• The net magnetic field due to a solenoid is the vector sum of the fields due to all the turns.
• Enamelled wires are used for winding so that turns are insulated from each other.

The magnetic field at a distance on the axis of the solenoid:

• The magnetic field on the axis at a far distance 'x' from the center of the solenoid is given as,
  
• The magnitude of the magnetic moment of the solenoid is given as,

⇒ m = n×(2l)×I×(πa2) = (total number of turns × current × cross-sectional area)
Where n = number of turns per unit length, I = current in the solenoid, 2l = length of the solenoid, and a = radius of the solenoid

Explanation:
Given B = magnitude of the magnetic field at a far distance along the axis of the solenoid
We know that the magnetic field on the axis at a far distance 'r' from the center of the solenoid is given as,
-----(1)
​Where n = number of turns per unit length, I = current in the solenoid, 2l = length of the solenoid, and a = radius of the solenoid
If the current in the solenoid is doubled then the magnetic field at that point is given as (I' = 2I),


-----(2)
By equation 1 and equation 2,
⇒ B' = 2B

• Hence, option 2 is correct.