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QUESTION: 1

A circular conductor of 1 cm radius has an internal magnetic field

where , r_{0} is the radius of the conductor and is the unit vector. The total current in the conductor is given by

Solution:

By Ampere's law,

Hence, current enclosed

Given, r_{0} = 1 cm = 0.01 m

QUESTION: 2

What is the value of mutual inductance between an infinitely long straight conductor along the y-axis and a rectangular single turn coil situated in x-y plane with its corners located at point (a, 0), (a + d, 0), (a, h) and (a + d, h) as shown in figure below?

Solution:

The mutual inductance is given by

Flux density at any point P in the x-y plane is

and

QUESTION: 3

Assertion (A): The force acting between two parallel wires carrying currents is directly proportional to the individual currents and inversely proportional to the square of the distance between them,

Reason (R): The force is repulsive if the two currents I_{1} and I_{2} are in the same directions and attractive if in opposite directions.

Solution:

The force acting between the two parallel wires carrying currents I_{2} and I_{2} respectively is given by

Thus,

Hence, assertion is a correct statement.

Reason is a false statement because F will be attractive if the two currents I_{2} and I_{2} will be in the same directions and repulsive if in opposite directions.

QUESTION: 4

The energy stored in a magnetic field is given by

Solution:

QUESTION: 5

Lorentz force law is

Solution:

QUESTION: 6

The equation is the generalization of

Solution:

QUESTION: 7

The unit of relative permeability is

Solution:

Relative permeability,

μ_{r} is a dimensionless quantity.

QUESTION: 8

Consider the volume current density distribution in cylindrical co-ordinates as

Where a and b are inner and outer radii of the cylinder as shown in figure below

Now, consider the value of magnetic field intensity in various regions I, II and III respectively obtained as:

Which of the above found values of H are correct for the respective regions?

Solution:

- For region-I (0 < r < a), J (r, ϕ, z) = 0

Using Ampere’s law, we have

or , H·2πr = 0 or H = 0 - For region - II

Again,

or,

- For region - III (b < r < ∞), J = 0

Again,

QUESTION: 9

Assertion (A): It is not possible to have isolated magnetic charges.

Reason (R): The magnetic flux lines always close upon themselves.

Solution:

Since, magnetic flux lines always close upon themselves therefore it is not possible to have isolated magnetic charges (or poles).

QUESTION: 10

Match List-l with List-lI and select the correct answer using the codes given below the fists:

List-l

A. Gauss’s law for magnetostatic fields

B. Gauss’s law for electrostatic fields

C. Conservativeness of electrostatic fields

D. Ampere's law

List-lI

Codes:

A B C D

(a) 5 4 1 2

(b) 3 1 4 5

(c) 3 4 1 5

(d) 5 1 4 2

Solution:

QUESTION: 11

The magnetic vector potential is given by

The total magnetic flux crossing the surface ϕ = π/2 , 1 ≤ ρ ≤ 2 m , 0 ≤ z ≤ 5 m is

Solution:

The total magnetic flux crossing the surface

ϕ = π/2 , 1 ≤ ρ ≤ 2 m , 0 ≤ z ≤ 5 m is given as:

= 3.75 Wb

QUESTION: 12

Which of the following is not a source of magnetostatic fields?

Solution:

An accelerated charge will produce both time varying electric and magnetic field called electromagnetic field.

QUESTION: 13

Consider the following statements associated with the characteristics of static magnetic field:

1. It is solenoidal.

2. Magnetic flux lines are not closed in certain cases.

3. The total number of flux lines entering a given region is equal to the total number of flux lines leaving the region.

4. It is conservative.

Which of the above statements is/are not correct?

Solution:

- Static magnetic field is non-conservative unlike static electric field. Hence, statement-4 is not correct.
- Magnetic flux lines are always closed. Hence, statement-2 is not correct.
- Statement 1 and 3 are correct.

QUESTION: 14

What are the units for the product of two values whose respective units are Henrys and Amperes?

Solution:

The Henry, the unit for mutual inductance is equivalent to V-sec/Ampere.

So, H x Ampere = Volt-sec = V-s

QUESTION: 15

What are the possible dimensions for a rectangular coil that has a magnetic flux of 9.5 webers when in a magnetic field of strength 19 Tesla at an angle of 60° from the perpendicular to the plane of the coil?

Solution:

Magnetic flux φ_{B} = BA cosθ

or,

Hence, the area of the rectangular coil should be 1 m^{2}. Only option (d) is matching the answer i.e. 250 cm x 40 cm

= 10000 cm^{2} = 1 m^{2}.

QUESTION: 16

What is the change in magnetic fiux in a coil of area 5 m^{2} as its orientation relative to the perpendicular of a uniform 3.0 T magnetic field changes from 45° to 90°?

Solution:

Flux ϕ = B A cosθ

At θ = 45°, ϕ_{1}= 3 x 5 x cos 45° = 11 Wb

At θ = 90°, ϕ_{2} = 3 x 5 x cos 90° = 0 Wb

∴ Change in flux = ϕ_{2} - ϕ_{1} = -11 Wb

QUESTION: 17

If a vector field is solenoidal, which of these is true?

Solution:

(Non-existence of monopole)

QUESTION: 18

If , the value of around the closed circular quadrant shown in the given figure is

Solution:

QUESTION: 19

The Maxwell’s equation, is based on

Solution:

QUESTION: 20

Given a vector field in cylindrical coordinates. For the contour as shown below, is

Solution:

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