Current loop as a magnetic dipole and its moment — practice questions

Question 1 · difficulty L1 · recall

The magnetic dipole moment of a single planar current loop is

• A. I/A directed in the loop plane
• B. IB directed along the current
• C. IA directed normal to the loop by the right-hand rule
• D. IA directed tangentially

Question 2 · difficulty L1 · understanding

For N identical turns carrying the same current, magnetic moment magnitude is

• A. IA/N
• B. NI/A
• C. N²IA
• D. NIA

Question 3 · difficulty L2 · understanding

A coil having 100 turns, area of $$5 \times 10^{-3} \mathrm{~m}^2$$, carrying current of $$1 \mathrm{~mA}$$ is placed in uniform magnetic field of $$0.20 \mathrm{~T}$$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $$90^{\circ}$$ is _________ $$\mu \mathrm{J}$$.

Question 4 · difficulty L2 · understanding

A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current is placed in a uniform magnetic field of $$1 \mathrm{~T}$$. Initially the magnetic dipole moment $$(\vec{M})$$ was directed along $$\vec{B}$$. Amount of work, required to rotate the coil through $$90^{\circ}$$ from its initial orientation such that $$\vec{M}$$ becomes perpendicular to $$\vec{B}$$, is ________ $$\mu$$J.

Question 5 · difficulty L2 · understanding

A wire of length $$314 \mathrm{~cm}$$ carrying current of $$14 \mathrm{~A}$$ is bent to form a circle. The magnetic moment of the coil is ________ A $$-\mathrm{m}^{2}$$. [Given $$\pi=3.14$$]

Question 6 · difficulty L2 · understanding

A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 10 3 cm 3 . If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0.75 A in the solenoid, the fractional change in the magnetic moment of the core would be approximately $$\left( {{x \over {499}}} \right)$$. Find the value of x.

Question 7 · difficulty L2 · understanding

Two short magnetic dipoles m 1 and m 2 each having magnetic moment of 1 Am 2 are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m 2 due to the presence of m 1 is ........... $$\times$$ 10 $$-$$7 Nm.

Question 8 · difficulty L2 · understanding

The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $$\mathrm{r}_{\mathrm{A}}=10$$ $$\mathrm{cm}$$ and $$\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$$ respectively are equal if : (Where $$\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$$ and $$\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$$ are number of turn and current of $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively)

• A. $$4 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
• B. $$2 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
• C. $$\mathrm{N}_{\mathrm{A}}=2 \mathrm{~N}_{\mathrm{B}}$$
• D. $$\mathrm{N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=4 \mathrm{~N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$

Question 9 · difficulty L2 · understanding

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $$4.0\times10^{-5}\mathrm{N~m~rad^{-1}}$$, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm$$^2$$) is :

• A. 1.5
• B. 2.0
• C. 0.5
• D. 1.0

Question 10 · difficulty L2 · understanding

Two concentric circular loops of radii $$r_{1}=30 \mathrm{~cm}$$ and $$r_{2}=50 \mathrm{~cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7 \mathrm{~A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

• A. $$\frac{7}{2} \hat{k} \,\mathrm{Am}^{2}$$
• B. $$-\frac{7}{2} \hat{k} \,\mathrm{Am}^{2}$$
• C. $${7}\, \hat{k} \,\mathrm{Am}^{2}$$
• D. $${-7}\, \hat{k} \,\mathrm{Am}^{2}$$