A small circular loop of conducting wire has radius a and carries… | JEE Main 2020 (9 Jan, Shift 2)

Q66JEE Main 2020 · 9 JAN · SHIFT 2Difficult

Current Loop as a Magnetic Dipole

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then:

Show answer and solution

Answer: (d)

Restoring torque for small $\theta$ : $\tau = -mB\theta$ with $m = I\pi a^2$ .
Moment of inertia about a diameter: $I_d = \frac{ma^2}{2}$ ( $m$ = mass).
$T = 2\pi\sqrt{\frac{I_d}{I\pi a^2 B}} = 2\pi\sqrt{\frac{m}{2\pi IB}}$
$T = \sqrt{\frac{4\pi^2 m}{2\pi IB}} = \sqrt{\frac{2\pi m}{IB}}$
So the answer is (d).

Report a mistake

More questions on Current Loop as a Magnetic Dipole

A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying…JEE Main 2020 (4 Sep, Shift 2)
In a hydrogen atom, an electron of charge e revolves in a orbit of radius r with speed v…MHT CET 2019 (3 May, Shift 1)
Torque acting on a rectangular coil carrying current ' i ' situated parallel to magnetic…MHT CET 2019 (2 May, Shift 2)
A circular coil and a square coil is prepared from two identical metal wires and a…MHT CET 2019 (3 May, Shift 1)
A square loop is carrying a steady current I and the magnitude of its magnetic dipole…JEE Main 2019 (10 Apr, Shift 2)
A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in…JEE Main 2019 (9 Apr, Shift 1)
A circular coil having N turns and radius r carries a current I. It is held in the XZ…JEE Main 2019 (8 Apr, Shift 1)
An insulating thin rod of length l has a linear charge density ρ(x) = ρ₀x/l on it. The…JEE Main 2019 (10 Jan, Shift 1)

Current Loop as a Magnetic Dipole question from JEE Main 2020 (9 Jan, Shift 2)

More questions on Current Loop as a Magnetic Dipole