A circular coil having 200 turns, $2.5 \times 10^{-4} \text{ m}^2$ area and carrying $100 \mu\text{A}$ current is placed in a uniform magnetic field of 1 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 ______ $\mu\text{J}$.

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Magnetic Effects of Current

A circular coil having 200 turns,

2.5 \times 1 0^{- 4} m^{2}

area and carrying

100 μ A

current is placed in a uniform magnetic field of 1 T. Initially the magnetic dipole moment (

M

) was directed along

B

. Amount of work, required to rotate the coil through

9 0^{\circ}

from its initial orientation such that

M

becomes perpendicular to

B

, is ______

μ J

Answer: 5

Solution

Work

= Δ U = - M B cos θ_{f} + M B cos θ_{i} = M B (cos 0^{\circ} - cos 9 0^{\circ}) = M B = N I A B

W = 200 \times (100 \times 1 0^{- 6}) \times (2.5 \times 1 0^{- 4}) \times 1 = 5 \times 1 0^{- 6} J = 5 μ J .

The value is

5.

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Integer answer

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