Question

A metallic block carrying current I is subjected to a uniform magnetic field $\overrightarrow{B}$ as shown in the figure. The moving charges experience a force $\overrightarrow{F}$ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be v

• A. $eVB\hat{k},ABCD$
• B. $eVB\hat{k},EFGH$
• C. $-eVB\hat{k},ABCD$
• D. $-eVB\hat{k},EFGH$

Answer 1

The correct option is D $-eVB\hat{k},EFGH$

As the block is of metal, the charge carriers are electrons, so for current along positive x-axis, the electrons are moving along negative x-axis, i.e. $\overrightarrow{v}=-v\hat{i}$
and, as the magnetic field is along the y-axis, i.e. $\overrightarrow{B}=B\hat{j}$
so,$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})forthiscaseyield\overrightarrow{F}=\left(e\right)[-v\hat{i}\times B\hat{j}]$
i.e., $\overrightarrow{F}=-evB\hat{k}[As\hat{i}\times \hat{j}=\hat{k}]$



As force on electrons is towards the face EFGH, the electrons will accumulate on it an hence it will acquire lower potential.