First slide

Motional EMF

Question

A metallic rod AB of length 1.5 m is made to move in a uniform magnetic field of 2 tesla with a velocity of 2 m/s as shown in figure. Then electro static field that appears in the rod is

Moderate

A

4 volt/m
B

3.5 volt/m
C

6 volt/m
D

2.5 volt/m

Solution

Due to the action of magnetic force $[(- e) \vec{V} \times \vec{B}]$ , free electron in the rod migrate to the end B and the rod becomes polarized. As a result an electro static field appears in the rod and net Lorentz force on each free electron becomes zero.
$∴ (- e) \vec{E} + (- e) \vec{V} \times \vec{B} = 0 \Rightarrow \vec{E} = - \vec{V} \times \vec{B} = \vec{B} \times \vec{V}$ $\Rightarrow E = v B = 2 \times 2 v / m = 4 v / m$

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