Assertion (A): A metallic rod of length L is rotated with a constant angular velocity ω about one of its ends in a uniform magnetic field B perpendicular to its plane of rotation. The induced EMF acro

Question

Assertion (A): A metallic rod of length $L$ is rotated with a constant angular velocity $ω$ about one of its ends in a uniform magnetic field $B$ perpendicular to its plane of rotation. The induced EMF across its ends is $\frac{1}{2} B ω L^{2}$ .

Reason (R): The free electrons in the rod experience a magnetic Lorentz force, causing them to accumulate at one end, leading to a potential difference.

TestHub · Accepted Answer

When a metallic rod rotates in a magnetic field, the free electrons within the rod move with the rod. Each electron experiences a magnetic Lorentz force $F = q (v \times B)$ .

This force causes charge separation, leading to an accumulation of electrons at one end and positive charge at the other, establishing an electric field and thus a potential difference (EMF).

The magnitude of this induced motional EMF for a rotating rod is indeed given by $E = \frac{1}{2} B ω L^{2}$ . Both assertion and reason are true, and the reason correctly explains the origin of the induced EMF.

Physics - EMI/AC Question with Solution | TestHub

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