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Question

A ring of radius R having a linear charge density λ moves towards a solid imaginary sphere of radius R2, so that the centre of the ring passes through the centre of sphere. The axis of the ring is perpendicular to the line joining the centres of the ring and the sphere. The maximum flux through the sphere in this process is


A
λRε0
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B
λR2ε0
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C
λπR4ε0
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D
λπR3ε0
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Solution

The correct option is D λπR3ε0
Electric flux will be maximum when maximum length of ring is inside the sphere.
This will occur when the length of the chord AB is maximum.

Now, maximum length of chord AB can be the diameter of the sphere.

Since, diameter of sphere is equal to radius of ring, hence it will form an equilateral triangle, each angle having 60.

In this case length of the arc of ring inside the sphere can be calculated as,

Arc length =2πR360×60=π3R

Thus, charge (q) on the arc in this situation is given as,
q=Arc length×λ

q=Rπ3λ

Thus, the maximum flux ϕmax through solid sphere is
ϕmax=qε0

ϕmax=Rπ3λε0

ϕmax=Rπλ3ε0

Hence, option (d) is correct answer.

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