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A non conducting disc carries a uniform surface charge density

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Solving time: 3 mins

A non conducting disc carries a uniform surface charge density $σ$ in the region defined by $a < x < b$ , where $x$ is the radial distance of apoint on the surface of the disc from its centre. The disc is made to rotate with an augular speed $ω$ about its central axis. Find the magnetic field at the centre $(O)$ of the disc.

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Book:

Physics for JEE Main and Advanced Magnetism and EMI (McGraw Hill)

Text solutionVerified

Consider a ring of radius

x

and width

d x

. Charge on the ring is

d q = σ \cdot 2 π x d x

Frquency of rotation is

f = \frac{ω}{2 π}

. Current associated with the thin ring of radius

x

d I = (d q) f = σω x d x

Magnetic field at the centre due to this current is

d B = \frac{μ _{0} ( d I )}{2 x} = \frac{μ _{0} σω}{2} d x

Adding contributions made by all such rings, gives

B = \int d B = \frac{μ _{0} σω}{2} \int_{a}^{b} d x = \frac{μ _{0} σω}{2} (b - a)

The field is normal to the plane of the ring.

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A non conducting disc carries a uniform surface charge density

σ

in the region defined by

a < x < b

, where

x

is the radial distance of apoint on the surface of the disc from its centre. The disc is made to rotate with an augular speed

ω

about its central axis. Find the magnetic field at the centre

(O)

of the disc.

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Discuss this question LIVE

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Question Text	A non conducting disc carries a uniform surface charge density $σ$ in the region defined by $a < x < b$ , where $x$ is the radial distance of apoint on the surface of the disc from its centre. The disc is made to rotate with an augular speed $ω$ about its central axis. Find the magnetic field at the centre $(O)$ of the disc.
Topic	Moving Charges and Magnetism
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	64

Text solutionVerified

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