Biot-Savart law and the current-carrying circular loop — practice questions

Question 1 · difficulty L1 · recall

In the Biot-Savart law, the magnetic field contribution dB from a current element is maximum when the element is oriented at what angle to the line joining it to the observation point?

• A. 90°
• B. 0°
• C. 30°
• D. 180°

Question 2 · difficulty L1 · understanding

Which change, by itself, doubles the magnetic field at the centre of a single circular loop?

• A. Doubling the radius while keeping the current fixed
• B. Doubling the current while keeping the radius fixed
• C. Halving the current and doubling the radius
• D. Doubling both current and radius

Question 3 · difficulty L2 · understanding

A circular loop of radius R carries current I. What is the magnetic field magnitude at its centre?

• A. μ0I/(4πR)
• B. μ0IR/2
• C. μ0I/(2R)
• D. μ0I/(2πR)

Question 4 · difficulty L2 · application

A coil has N closely wound circular turns of radius R carrying current I. What field is produced at the common centre?

• A. μ0I/(2NR)
• B. Nμ0I/(4πR)
• C. N²μ0I/(2R)
• D. Nμ0I/(2R)

Question 5 · difficulty L2 · understanding

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm . The magnetic field at the mid point between the two wires is $\_\_\_\_$ $\mu \mathrm{T}$. $$\left(\frac{\mu_{\mathrm{o}}}{4 \pi}=10^{-7} \mathrm{~N} / \mathrm{A}^2\right)$$

• A. 30
• B. 300
• C. 150
• D. 0.0

Question 6 · difficulty L2 · understanding

The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16 \mu \mathrm{~T}$. The magnetic field at a distance $x=\sqrt{3} R$ on its axis from the centre is $\_\_\_\_$ $\mu \mathrm{T}$.

• A. 8
• B. 2
• C. 4
• D. $2 \sqrt{2}$

Question 7 · difficulty L2 · understanding

An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The magnetic field on the $$y$$-axis at a distance of $$0.5 \mathrm{~m}$$ from the elements $$\Delta x$$ of $$1 \mathrm{~cm}$$ length is:

• A. $$10 \times 10^{-8} \mathrm{~T}$$
• B. $$8 \times 10^{-8} \mathrm{~T}$$
• C. $$4 \times 10^{-8} \mathrm{~T}$$
• D. $$12 \times 10^{-8} \mathrm{~T}$$

Question 8 · difficulty L2 · understanding

Two insulated circular loop A and B of radius '$$a$$' carrying a current of '$$\mathrm{I}$$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

• A. $$\frac{\sqrt{2} \mu_0 I}{a}$$
• B. $$\frac{\mu_0 I}{\sqrt{2} a}$$
• C. $$\frac{\mu_0 \mathrm{I}}{2 \mathrm{a}}$$
• D. $$\frac{2 \mu_0 I}{a}$$

Question 9 · difficulty L2 · understanding

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

• A. uniform in the region $$r < a$$ and inversely proportional to distance $$r$$ from the axis, in the region $$r > a$$
• B. zero in the region $$r < a$$ and inversely proportional to $$r$$ in the region $$r > a$$
• C. directly proportional to $$r$$ in the region $$r < a$$ and inversely proportional to $$r$$ in the region $$r > a$$
• D. inversely proportional to $$r$$ in the region $$r < a$$ and uniform throughout in the region $$r > a$$

Question 10 · difficulty L2 · understanding

A long solenoid is formed by winding 70 turns cm$$^{-1}$$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($$\mu_0=4\pi\times10^{-7}$$ TmA$$^{-1}$$)

• A. $$88\times10^{-4}$$ T
• B. $$1232\times10^{-4}$$ T
• C. $$176\times10^{-4}$$ T
• D. $$352\times10^{-4}$$ T