Physics: CUET Mock Test - 2 - CUET MCQ

A scalar quantity is a quantity with magnitude only but no direction. But a vector quantity possesses both magnitude and direction. An electric field has a very specific direction (away from a positive charge or towards a negative charge). Hence electric field is a vector quantity. Moreover, we have to use a vector addition for adding two electric fields.

dB = 

dB = 1.4 × 10^-9 T.

Let the distance between any two charges is d. Therefore the net potential energy of the system is  But the total energy of the system is zero. So, -qQ - qQ + q²/2 = 0 hat means q = 4Q, i.e. q/Q = 4.

We can consider the relation that includes power and resistance, i.e. Power = voltage²/resistance . Since, the resistors are connected in parallel, the voltage across them will be the same. From this relation, power and resistance are inversely proportional to each other.
Thus,  
So, the power dissipated is in the ratio is 1:3.

Kirchhoff’s Law is used to analyze circuits. This law is important because they represent connections of a circuit. Kirchhoff’s Law provide the constraints that let us find the current flowing and voltage across every circuit element.

The electric field at a distance of r from a charge q is equal to  Let the electric field intensity will be zero at a distance of x cm from +4q charge, so the fields due to the two charges will balance each other at that point. Therefore  Solving this we get x=20cm. Therefore the point will be 20cm away from the +4q charge.

A non-polar substance consists of a huge number of dipoles in it, but they are oriented randomly and hence the net dipole moment of the substance becomes 0 and it acts as a non-polar substance. But if it is placed in an electric field, the dipoles present in it will orient themselves in the direction of the field and hence a net dipole moment will be observed, known as induced dipole moment. No current flow or oscillation of the substance will be observed.

Net electrostatic field is zero in the interior of a conductor. When a conductor is placed in an electric field, its free electrons begin to move in the opposite direction. Negative charges are induced on the left end and positive charges on the right end of the conductor. The process continues until the electric field set up by induced charges becomes equal and opposite the external field.

The equivalent overall resistance of the parallel combination is:

R1 is in series with R2; So, R3 = R1 + R2 = 10 + 20 = 30 ohms.
Now, we can employ the method of cross-multiplication:
For 20 ohms resistor → 30 W power consumed
For 30 ohms resistor combination → x
20x = 30 × 30
x = (30 × 30)/20
x = 45
Therefore, the power consumed by the parallel combination is 45 ohms.

Kirchhoff’s 2^nd year is applied in a closed loop. Kirchhoff’s 2^nd law supports the law of conservation of energy. This means that energy is neither created nor destroyed in the closed loop. Whatever energy enters the loop, same amount leaves the loop.

Electric field intensity is defined as the force on a unit positive charge kept in an electric field. Hence we can simply consider its dimension as (the dimension of force/the dimension of charge). The dimension of force is [MLT^-2] and the dimension of charge is [IT]. Therefore the dimension of field intensity is [M L T^-3 I^-1].

Magnetic permeability of free space is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. The SI unit of permeability is weber ampere^-1 metre^-1 (Wb A^-1 m^-1) or tesla ampere^-1 meter (T A^-1 m).

Ampere’s circuital law states that the line integral of magnetic field around any closed path in vacuum is equal to μ₀ times the total current passing the closed path. It is given by: ∮ B .dl = μ₀I
Ampere’s circuital law is analogous to Gauss’s law in electrostatics.

Torque = NIBA sinθ.
Torque = 50 × 20 × 0.2 × 200 × 10^-4 × sin (90)
Torque = 4Nm.

The magnetic flux through a surface is the surface integral of the normal component of the magnetic field flux density passing through that surface. The SI unit of magnetic flux is weber (Wb). One weber is the flux produced when a uniform magnetic field of one tesla acts normally over an area of 1 cm².

E=-(dV/dx) where E is the field intensity, V is potential and x is distance. Therefore unit of electric field intensity will be (unit of potential/unit of distance) = V/m. Electric flux has unit V * m, V is the unit of electric potential whereas charge has a unit of Coulomb or esu.

Right-hand thumb rule can be used to find the direction of the magnetic field at a point near a current-carrying conductor. Right hand rule states that, if the thumb of the right hand is in the direction of the current flow then, the curl fingers show the direction of the magnetic field.

The magnetic field inside a pipe, i.e. inside a hollow cylindrical wire is zero. This is due to the symmetry of the situation (pipe). The pipe can be considered as a series of thin wires arranged in a circle.

Torque (Max) = NIBA.
Τ_max = 400 × 10³ × 0.2 × 320 × 10^-4
T_max = 2560 Nm.

Magnetic flux = Magnetic field × Area.
Flux = 
Flux = 
Flux = [M L² A^-1 T^-2].

The electric field at the surface of a charged conductor is proportional to the surface charge density. The electric field is zero inside the conductor and just outside, it is normal to the surface. The contribution to the total flux comes only from its outer cross-section.

Torque on a planar current loop depends upon current, the strength of the magnetic field, area of the loop and the orientation of the loop in the magnetic field. It is independent of the shape of the loop.

1 Wb = 1 T × 1 m²
Wb = 10⁴ G × 10⁴ cm².
1 Wb = 10⁸ Maxwell.

The principle of superposition applies to both fields. This is because the magnetic field is linearly related to its source, namely, the current element and the electrostatic field is related linearly to its source, the electric charge.

In classical electrodynamics, the magnetic field given by a current loop and the electric field caused by the corresponding dipoles in sheets are very similar, as far as we are far away from the loop, which enables us to deduce Ampere’s magnetic circuital law from the Biot-Savart law easily.

The SI unit of magnetic pole strength is ampere meter (Am).
The strength of a magnetic pole is said to be one-ampere meter if it repels an equal and similar pole with a force of 10^-7 N when placed in vacuum at a distance of one meter from it.

A normal to a plane can be drawn from either side. If the normal drawn to a plane points out in the direction of the field, then θ = 0^o and the flux are taken as positive. If the flux is positive and increasing the voltage will be negative.

The potential difference between any two points on an equipotential surface is zero.
Work done=Test charge x potential difference(0)
=Zero .

The magnetic field due to a long straight wire of radius x carrying a current I at a point distant r from the axis of the wire is given by:
B_in = 
B_in = 
The magnetic field at a distance of r = x/4:
B1 = 
The magnetic field at a distance of r = 8x:

The phenomenon of making a region free from any electric field is called electrostatic shielding. It is based on the fact that the electric field vanishes inside the cavity of a hollow conductor.