This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Ampere’s Circuital Law”.

1. Identify the expression for ampere’s circuital law from the following?

a) ∮ B .dl = μ_{0}I

b) ∮ B .dl = \( \frac {\mu_0}{I}\)

c) ∮ B .dl = 2μ_{0}I

d) ∮ B .dl = 4μ_{0}I

View Answer

Explanation: Ampere’s circuital law states that the line integral of magnetic field around any closed path in vacuum is equal to μ

_{0}times the total current passing the closed path. It is given by:

∮ B .dl = μ

_{0}I

Ampere’s circuital law is analogous to Gauss’s law in electrostatics.

2. What is the magnetic field inside a pipe?

a) Unity

b) Infinity

c) Zero

d) Two

View Answer

Explanation: 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.

3. Which one of the following graphs depict the magnetic field B at a distance r from a long straight wire carrying current varies with distance r?

a)

b)

c)

d)

View Answer

Explanation: The magnetic field B at a distance r from a long straight wire carrying current I is given by:

B = \(\frac {\mu_0 2I}{4\pi r}\)

B = \(\frac {\mu_0 I}{2\pi r}\)

From this, we understand that the magnetic field is inversely proportional to the distance r.

B ∝ \(\frac {1}{r}\)

4. The angle at which a charged particle moves through a magnetic field with a velocity, having zero magnetic force is 180^{o}.

a) True

b) False

View Answer

Explanation: This statement is false. When a charged particle is moving through a magnetic field with a velocity and has a zero magnetic force, then the angle at which the charged particle should move is 0

^{o}or 90

^{o}.

5. Which law can ampere’s circuital be derived from?

a) Gauss Law

b) Newton’s Law

c) Kirchhoff’s Law

d) Biot-Savart Law

View Answer

Explanation: 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.

6. A long straight wire of radius x carries a steady current I. The current is uniformly distributed across its cross section. Calculate the ratio of the magnetic field at \(\frac {x}{4}\) and 8x.

a) 4

b) 3

c) 2

d) 1

View Answer

Explanation: 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}= \(\frac {\mu_o Ir}{2\pi x^2}\) (r < x)

B

_{in}= \(\frac {\mu_o I}{2\pi r}\) (r > x)

The magnetic field at a distance of r = \(\frac {x}{4}\):

B1 = \(\frac {\mu_o I (\frac {x}{4})}{2\pi x^2} = \frac {\mu_o I}{8\pi x}\)

The magnetic field at a distance of r = 8x:

B2 = \(\frac {\mu_o I}{2\pi (8x)} = \frac {\mu_o I}{16\pi x}\)

Therefore, \(\frac {B1}{B2} = \frac {\frac {\mu_o I}{8\pi x}}{\frac {\mu_o I}{16\pi x}}\)

\(\frac {B1}{B2} = \frac {16}{8}\) = 2

7. Find the true statement.

a) The force between two parallel current carrying wires is independent of the radii of the wires

b) The force between two parallel current carrying wires is independent of the length of the wires

c) The force between two parallel current carrying wires is independent of the magnitude of currents

d) The force between two parallel current carrying wires is independent of their distance of separation

View Answer

Explanation: The force between two parallel current carrying wires is independent of the radii of the wires.

From Ampere’s circuital law, the magnitude of the field due to the first conductor can be given by:

B = \(\frac {\mu_o I_1}{2\pi d}\)

The force between the parallel plates is given by:

B= \([\frac {\mu_o I_1 I_2}{2\pi d}] \) L

From this equation, we understand that the force between the parallel current carrying wires does not depend on the ‘radii’.

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