KCET · Physics · Electrostatics

A copper rod \(A B\) of length \(l\) is rotated about end \(A\) with a constant angular velocity \(\omega\). The electric field at a distance \(x\) from the axis of rotation is

A \(\frac{m \omega^{2} x}{e}\)
B \(\frac{m \omega x}{e}\)
C \(\frac{m x}{\omega^{2} l}\)
D \(\frac{m e}{\omega^{2} x}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{m \omega^{2} x}{e}\)

Step-by-step Solution

Detailed explanation

In circular motion, net force on the particle is given as
\(F_{c}=\frac{m v^{2}}{r}=m \omega^{2} r\)
where, \(\omega\) is angular speed.
When the rod rotates, electrons in it also rotates which produce electric field \(E\) at a distance \(x\).
So, force on electron,
\(F_{e}=e E\)
This force provide the centripetal force,
i.e., \(\quad F_{e}=F_{c}\)
or
\(e E=m \omega^{2} x\)
or
\(E=\frac{m \omega^{2} x}{e}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

List-I	List-II
(a)	Angle of reflection	(i)	\(60^\circ\)
(b)	Value of \(\alpha\)	(ii)	\(120^\circ\)
(c)	Angle of deviation	(iii)	\(30^\circ\)

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