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Physics: CUET Mock Test - 1 - Question 1

The amount of force exerted on a unit positive charge in an electric field is known as _____

Detailed Solution for Physics: CUET Mock Test - 1 - Question 1

The zone near a charge where its attraction or repulsion force works, is known as the electric field of that charge. Theoretically, it is up to infinite but practically it has limitations. If a unit positive charge is kept in that field, it will undergo some force which is known as electric field intensity at that point.

Physics: CUET Mock Test - 1 - Question 2

An infinitly long wire is charged uniformly with charge density λ and placed in air, the electric field at distance r from wire will be:

Detailed Solution for Physics: CUET Mock Test - 1 - Question 2

Concept:

Electric field:

  • ​It is defined as the force per unit of positive charge.
  • Formula, Electric field, E = F/q where F = force, q = positive charge
  • The SI unit of electric charge is N/C.

Electric field due to an infinitely long straight wire:

  • Consider an infinitely long straight, uniformly charged wire. Let the linear charge density of this wire be λ. P is the point that is located at a perpendicular distance from the wire. The distance between point P and the wire is r.

  • The electric field is due to an infinitely long straight wire, .

Explanation:
Assuming the wire is infinitely long, the electric field will be radial and will have a magnitude given by:

E =

where
λ is the linear charge density of the wire,
ε₀ is the permittivity of free space,
r is the distance from the wire.

  • The direction of the electric field will be radial and pointing away from the wire if the charge on the wire is positive and towards the wire if the charge on the wire is negative.
  • Note that the above formula assumes that the wire is thin compared to the distance from it, and that the electric field is being measured at a point far away from the ends of the wire. If these assumptions are not satisfied, the electric field may be different.
Physics: CUET Mock Test - 1 - Question 3

Two point charges (-q) and (+4q) are placed at separation 'r'. Where should a third charge be placed so that entire system of charges becomes in equilibrium?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 3

Calculation:

Let a charge "Q" is placed at a distance of "x" from (-q).

Let the force exerted by "-q" be F1 and "4q" be F2 on "Q".

To make the system in equilibrium, the net force acting on "Q" should be zero.

i.e., F1 + F2 = 0.-----(1)

F1 = K(-q)Q/x2

F2 = K(4q)Q/(r + x)2

Putting the value of F1 and F2 in equation (1), we get,

K(-q)Q/x2 + K(4q)Q/(r + x)2 = 0

(x + r)/x = 2

x = r

The charge "Q" is placed at a distance of "r" from charge "-q" on the extreme side of (-q).

The correct answer is option (1).

Physics: CUET Mock Test - 1 - Question 4

The variation of electric field with respect to distance from centre of a charged conducting spherical shell of radius R is given by :

Detailed Solution for Physics: CUET Mock Test - 1 - Question 4

Concept:

  • For a conducting spherical shell of radius R that carries a charge Q, the electric field inside the shell is zero.
  • And outside the shell, the electric field behaves as if all the charge Q is concentrated at the center of the shell.
  • Thus, the electric field outside the shell, at a distance r from the center, is given by Coulomb's law:

E = kQ/r2
where k is the Coulomb constant.

Therefore, the electric field outside the shell varies inversely with the square of the distance from the center of the shell.
That is, as the distance from the center of the shell increases, the electric field strength decreases rapidly.
So, the plot of electric field w.r.t the distance "r" would be,

The correct answer is option "2"

Physics: CUET Mock Test - 1 - Question 5
A conducting sphere is charged. If the electric field at a distance 20 cm from the centre of the sphere is 1.2 × 103 NC-1 and points radially inwards, the net charge on the sphere is:
Detailed Solution for Physics: CUET Mock Test - 1 - Question 5

Concept:

We know that for a conducting sphere, the electric field outside the sphere is the same as the field due to a point charge located at the center of the sphere. So, we can use the formula for the electric field due to a point charge to find the net charge on the sphere.

The electric field due to a point charge q at a distance r from it is given by:

E = k*q/r2

where k is the Coulomb constant.

In this case, the electric field at a distance of 20 cm from the center of the sphere is given as 1.2 × 103 NC-1, and it points radially inwards.

This means that the point charge at the center of the sphere is negative.

So, we have:

E = k*q/r2

= q = ------(1)

Calculation:

Given that

E = 1.2 × 103 NC-1

r = 20 cm = 0.2 m.

k = 4.5 × 109

Substituting values of k, r, E in the equation we get,

q =

=

= 5.33 ×10-9 C

Since the point charge at the center of the sphere is negative.

q = - 5.3 ×10-9 C

The correct answer is option (4)

Physics: CUET Mock Test - 1 - Question 6

A parallel plate capacitor having cross-sectional area 'A' and separated by distance 'd' is filled by copper plate of thickness b. It's capacitance is :

Detailed Solution for Physics: CUET Mock Test - 1 - Question 6

Concept:
The capacitance of a parallel plate capacitor is given by the formula:

C = εA/d
where
C is the capacitance,
ε is the permittivity of the medium between the plates,
A is the area of each plate, and d is the distance between the plates.

Calculation:
When a copper plate of thickness b is placed between the plates of the capacitor, the distance between the plates effectively reduces to d' = d - b, where b is the thickness of the copper plate. The permittivity of copper is very close to that of vacuum, so we can assume that the permittivity between the plates remains the same.

Therefore, the new capacitance of the capacitor is given by:
C' = εA/d'
C' = εA/(d - b)
C' =
The correct answer is option (2)

Physics: CUET Mock Test - 1 - Question 7

Conductivity of semiconductors _______ with temperature.

Detailed Solution for Physics: CUET Mock Test - 1 - Question 7

Semiconductors: A semiconductor is a material whose conductivity lies in between those of insulators and good conductors.

Examples: germanium and silicon.

In terms of energy band, semiconductors are materials that have almost an empty conduction band and an almost filled valence band with a very narrow energy gap (of the order of 1 eV) separating the two. At 0 K there are no electrons in the conduction band and the valence band is completely filled.

However, with the rise of temperature, some of the electrons from the valence band go to the conduction band overcoming the gap. So the conductivity of semiconductors increases with temperature.

Hence the correct answer is option 3.

Physics: CUET Mock Test - 1 - Question 8

Germanium is an example of

Detailed Solution for Physics: CUET Mock Test - 1 - Question 8

Semiconductors: A semiconductor is a material whose conductivity lies in between those of insulators and good conductors.
Examples: germanium and silicon.

Hence the correct answer is option 3.

Physics: CUET Mock Test - 1 - Question 9

In terms of energy bands, _______ have a full valence band

Detailed Solution for Physics: CUET Mock Test - 1 - Question 9

Insulators: Insulators are those materials in which the valence electrons are bonded very tightly to their parent atoms and there are no free electrons.
A large electric field is required to remove the electrons from the attraction of the nuclei.
In terms of energy bands, insulators (a) have a full valence band and (b) have an empty conductor band.

Hence the correct answer is option 2.

Physics: CUET Mock Test - 1 - Question 10

Conductors are those which have ________ valence and conduction bands.

Detailed Solution for Physics: CUET Mock Test - 1 - Question 10

On the basis of the band theory of solids, the solids are classified as -
(i) conductors, (ii) insulators, and (iii) semiconductors.

(i) Conductors or metals: Conducting materials are those in which plenty of free electrons are available for electric conduction.
In terms of energy bands, it means that conductors are those which have overlapping valence and conduction bands.

Hence the correct answer is option 2.

Physics: CUET Mock Test - 1 - Question 11

Which of the following in not a classification of solids, (according to the band theory)

Detailed Solution for Physics: CUET Mock Test - 1 - Question 11

On the basis of the band theory of solids, the solids are classified as -
(i) conductors, (ii) insulators, and (iii) semiconductors.
The superconductor is not included among these.

Hence the correct answer is option 4.

Physics: CUET Mock Test - 1 - Question 12

Which among the following molecule is not a dipole?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 12

Though water and ammonia are covalent molecules, they have a net dipole moment due to their distorted structure than the ideal one. Hydrochloric acid has a linear molecular structure but its net dipole moment is towards the Hydrogen atom. But methane has a symmetrical tetrahedral structure and its net dipole moment is zero hence it doesn’t behave as a permanent dipole. Methane solvents are therefore non-polar solvents.

Physics: CUET Mock Test - 1 - Question 13

Electric potential due to a point charge q at a distance r from the point is _______ (in the air).

Detailed Solution for Physics: CUET Mock Test - 1 - Question 13

Force on a unit point charge kept at a distance r from the charge = q/r2. Therefore, work done to bring that point charge through a small distance dr =(q/(r2)) * (-dr). Therefore, the potential of that point is =

Physics: CUET Mock Test - 1 - Question 14

In series connection of resistors, what happens to the current across each resistor?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 14

When the resistors are connected in series, and current is passed through them, the current passing through each of the resistor is the same. This is because, the resistors are connected end to the end and, therefore, there is only one path for the current to flow through.

Physics: CUET Mock Test - 1 - Question 15

Which among the following is true?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 15

According to Kirchhoff’s first law, the current flowing towards the junction is equal to the current leaving the junction. Mathematically, this law can be expressed as ∑nK – 1 IK = 0 (where n is the number of branches carrying current towards or away from the junction).

Physics: CUET Mock Test - 1 - Question 16

The direction of electric field created by a negative charge is _______

Detailed Solution for Physics: CUET Mock Test - 1 - Question 16

If a unit positive charge is kept near a negative charge, the unit positive charge will be attracted towards the negative charge. That means the electric field is towards the negative charge. But in case of positive charge, the field is directed away from the charge.

Physics: CUET Mock Test - 1 - Question 17

What is the dimension of the dipole moment?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 17

The dipole moment is defined as the product of a charge and distance. The dimension of charge (current*time) is [I T] and the dimension of distance is [L]. Therefore the dimension of dipole moment is [L T I]. Its unit in the CGS and the SI system are esu*cm and C*m respectively.

Physics: CUET Mock Test - 1 - Question 18

Calculate electric potential due to a point charge of 10C at a distance of 8cm away from the charge.

Detailed Solution for Physics: CUET Mock Test - 1 - Question 18

In the SI system, electric potential due to a point charge at a distance r is Substituting the values, we get potential=  Though in practice, this huge value of electric potential is not present.

Physics: CUET Mock Test - 1 - Question 19

What is the equivalent resistance of series combination of 3 resistors?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 19

When three resistors are connected in series, then the equivalent resistance of this combination is Rs = R1 + R2 + R3. So, if 3 resistors having resistances 10, 15, and 20 ohms, are connected in series, then equivalent resistance of this combination is Rs = 10 + 15 + 20 = 45 ohms.

Physics: CUET Mock Test - 1 - Question 20

The equation → ∑e = ∑IR is applicable to which law?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 20

The equation → ∑e = ∑IR is applicable to Kirchhoff’s second law. This law is also known as Kirchhoff’s loop rule. This expression tells us that in a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the products of the resistance and currents flowing through them.

Physics: CUET Mock Test - 1 - Question 21

Electric field inside a hollow conducting sphere ______

Detailed Solution for Physics: CUET Mock Test - 1 - Question 21

According to Gauss’s law, if there is no charge inside a closed surface, the field inside the closed surface will always be zero. We know the charge is distributed on the outer surface of a conducting hollow sphere because the charges want to maintain maximum distance among them due to repulsion. So there is no charge inside the sphere and hence no electric field.

Physics: CUET Mock Test - 1 - Question 22

If the force acting on a point charge kept on the axis of an electric dipole is F, what will be the amount of force if the distance of the point charge is doubled from the dipole?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 22

If the distance of a point charge, kept on the axis of a dipole, is sufficiently large than the separation between the charges of a dipole, then it can be shown that electric field E at a distance r from the dipole varies as E α 1/(r3). Now if the distance becomes 2r, electric field intensity will decrease by a factor of 2= 8 times. Therefore the force F will now become F/8.

Physics: CUET Mock Test - 1 - Question 23

What is the amount of work done to bring a charge of 4 * 10-3C charge from infinity to a point whose electric potential is 2 * 102V?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 23

Work done = potential*charge by definition. We know that the potential of a point is the amount of work done to bring a unit charge from infinity to a certain point. Therefore, work done W = q * V = 4 * 10-3 * 200J = 0.8J. The work done is positive in this case.

Physics: CUET Mock Test - 1 - Question 24

Identify the combination which is not a series connection.

Detailed Solution for Physics: CUET Mock Test - 1 - Question 24

Domestic appliances in a house are connected in parallel combinations, and not in series combinations. This arrangement is done so that each of the appliances can switched on and off independently, which is essential in a house’s wiring.

Physics: CUET Mock Test - 1 - Question 25

Identify the correct statement from the following.

Detailed Solution for Physics: CUET Mock Test - 1 - Question 25

According to sign convention while traversing a closed loop (in clockwise or anti-clockwise direction), if positive pole of the cell is encountered first then its emf is negative or else, it will be positive.

Physics: CUET Mock Test - 1 - Question 26

Electric field due to a uniformly charged hollow sphere at a distance of r (where r is greater than the radius of the sphere) is __________

Detailed Solution for Physics: CUET Mock Test - 1 - Question 26

If the total charge of the sphere is q then the electric field at a distance of r is equal to  Therefore the electric field is proportional is (1/(r2)) (if r > radius of the sphere). But if r < radius of the sphere the electric field will be zero i.e. electric field inside a hollow sphere is always zero.

Physics: CUET Mock Test - 1 - Question 27

If electric field intensity at a certain distance from a dipole on its axis is E1 and at the same distance but on the perpendicular bisector of the dipole is E2, then __________

Detailed Solution for Physics: CUET Mock Test - 1 - Question 27

If the dipole moment of a dipole is p, then electric field intensity at a distance r from the dipole on its axis will be (2p/(r3)). But electric field intensity at a distance r from the dipole on its perpendicular bisector is (P/(r3)). Both the formulas are derived by assuming r >> length of the dipole. Thus E1= 2P/r3 and E2 = P/r3 and hence E1 = 2 E2.

Physics: CUET Mock Test - 1 - Question 28

Two point charges 10C and -10C are placed at a certain distance. What is the electric potential of their midpoint?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 28

Electric potential is a scalar quantity and its value is solely dependent on the charge near it and the distance from that charge. In this case, the point is equidistant from the two point charges and the point charges have the same value but opposite nature. Therefore equal but opposite potentials are generated due to the charges and hence the net potential at midpoint becomes zero.

Physics: CUET Mock Test - 1 - Question 29

Three equal positive charges are kept at the corners of an equilateral triangle. What will be the vector sum of the forces acting on the particles?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 29

The magnitude of the force acting on each of the charges will be the same and they will differ from each other by 120 degrees. Therefore their resultant force will always be zero.

Physics: CUET Mock Test - 1 - Question 30

Which among the following is false?

Detailed Solution for Physics: CUET Mock Test - 1 - Question 30

Coulomb force is a strong force. It can be shown that the Coulomb force between two electrons is 1043 times than gravitational force. All the other options are basic properties of Coulomb’s Law.

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