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Electromagnetic Waves

Combination of Electric and Magnetic field

Two identical small balls, made of insulting material are atta

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Solving time: 4 mins

Two identical small balls, made of insulting material are attached to the ends of a light insulating rod of length d. The rod is suspended from the ceiling by a thin torsion free fibre as shown in figure. Each ball is given a charge $q$ . There is a uniform magnetic field $B_{0}$ , pointing vertically down, in a cylindrical region of radius $R$ . The fibre is along the axis of the cylindrical region. The system is initially at rest. Now the magnetic field is suddenly switched off. Calculate the angular velocity acquired by the system. Each ball has mass $m$ .

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Problems in Physics II for IIT JEE (McGraw Hill)

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Two identical small balls, made of insulting material are attached to the ends of a light insulating rod of length d. The rod is suspended from the ceiling by a thin torsion free fibre as shown in figure. Each ball is given a charge

q

. There is a uniform magnetic field

B_{0}

, pointing vertically down, in a cylindrical region of radius

R

. The fibre is along the axis of the cylindrical region. The system is initially at rest. Now the magnetic field is suddenly switched off. Calculate the angular velocity acquired by the system. Each ball has mass

m

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

When the magnetic field is switched off, an electric field is induced. The electric field

(E)

on a circle of radius

\frac{d}{2}

is given by

E \cdot 2 π (\frac{d}{2}) = π R^{2} \frac{Δ B}{Δ t}

∴ E = \frac{R ^{2}}{d} \frac{Δ B}{Δ t}

Electric force on each ball;

F_{e} = Eq

Impulse on each ball

= Eq Δ t = q \cdot \frac{R ^{2}}{d} (Δ B)

Angular impulse on each ball

= q \cdot \frac{R ^{2}}{d} (Δ B) \cdot \frac{d}{2}

Total angular impulse on both balls

= q R^{2} Δ B

Since

Δ B = B_{0}

∴

Angular Impulse

= q R^{2} B_{0}

Change in angular momentum

= q R^{2} B_{0}

2 \cdot m (\frac{d}{2})^{2} ω ω = q R^{2} B_{0} = \frac{2 q R ^{2} B _{0}}{m d ^{2}}

\Rightarrow ω = \frac{2 q R ^{2} B _{0}}{m d ^{2}}

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Question Text	Two identical small balls, made of insulting material are attached to the ends of a light insulating rod of length d. The rod is suspended from the ceiling by a thin torsion free fibre as shown in figure. Each ball is given a charge $q$ . There is a uniform magnetic field $B_{0}$ , pointing vertically down, in a cylindrical region of radius $R$ . The fibre is along the axis of the cylindrical region. The system is initially at rest. Now the magnetic field is suddenly switched off. Calculate the angular velocity acquired by the system. Each ball has mass $m$ .
Topic	Electromagnetic Waves
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	59

Text solutionVerified

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