Ampere's circuital law; straight wire and solenoid — practice questions

Question 1 · difficulty L1 · recall

Ampere's circuital law relates the closed-loop integral ∮B·dl to

• A. the total charge enclosed
• B. the magnetic flux through the loop
• C. μ0 times the net current enclosed
• D. the electric potential around the loop

Question 2 · difficulty L1 · understanding

Around a long straight current-carrying wire, magnetic field lines are

• A. radial straight lines
• B. parallel to the wire
• C. ellipses with the wire at one focus
• D. concentric circles centred on the wire

Question 3 · difficulty L2 · understanding

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4} ~\mathrm{Tesla}$. If the solenoid carries a current of 0.29 A , then the length of the solenoid is _______ $\pi \mathrm{cm}$.

Question 4 · difficulty L2 · understanding

A solenoid of length $$0.5 \mathrm{~m}$$ has a radius of $$1 \mathrm{~cm}$$ and is made up of '$$\mathrm{m}$$' number of turns. It carries a current of $$5 \mathrm{~A}$$. If the magnitude of the magnetic field inside the solenoid is $$6.28 \times 10^{-3} \mathrm{~T}$$ then the value of $$\mathrm{m}$$ is __________.

Question 5 · difficulty L2 · understanding

A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

• A. $\frac{\mathrm{B}^2 \mathrm{~A} l}{4 \mu_0}$
• B. $\frac{\mathrm{B}^2 \mathrm{~A} l}{2 \mu_0}$
• C. $\frac{\mathrm{B}^2 \mathrm{~A} l}{\mu_0}$
• D. $\mathrm{B}^2 \mathrm{Al}$

Question 6 · difficulty L2 · understanding

What is the magnetic field at distance r from a very long straight wire carrying current I?

• A. μ0I/(2πr)
• B. μ0I/(4πr²)
• C. μ0Ir/(2π)
• D. μ0I/(2r)

Question 7 · difficulty L2 · application

For an ideal long solenoid with n turns per unit length carrying current I, the field well inside is

• A. μ0I/(2πn)
• B. μ0nI
• C. μ0n/I
• D. μ0I/n

Question 8 · difficulty L3 · understanding

A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by $${N \over {12}}{\mu _0}aJ$$, then the value of N is ______________.

Question 9 · difficulty L3 · understanding

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is: A. maximum at either ends of the conductor and minimum at the midpoint B. maximum at the axis of the conductor C. minimum at the surface of the conductor D. minimum at the axis of the conductor E. same at all points in the cross-section of the conductor Choose the correct answer from the options given below:

• A. B, C Only
• B. E Only
• C. A, D Only
• D. D Only

Question 10 · difficulty L3 · understanding

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is

• A. $\frac{\mathrm{N}^2}{2 \pi} \mathrm{q} \omega$
• B. $\frac{\mathrm{N}}{2 \pi} \mathrm{q} \omega$
• C. $\mathrm{\frac{2 \pi}{N} q \omega}$
• D. $\frac{\mathrm{N}}{\pi} \mathrm{q} \omega$