Question 114: Electromagnetic Induction

Question

Consider a thin metallic sheet perpendicular to the plane of the paper
moving with speed
‘v’
in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $\sigma $
1
and $\sigma $
2
are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l82xh0bw/491f70cf-0c05-4298-9e50-794d8f93289c/d08fd0e0-34e3-11ed-b84c-a3c7c2456516/file-1l82xh0by.png?format=png)

Accepted Answer

Magnetic force on electron
$\overrightarrow F $ = $-$ e $\left( {\overrightarrow V  	imes \overrightarrow B } ight)$
F = eVB   [As ${\overrightarrow V }$ and ${\overrightarrow B }$ are perpendicular]
Also,   F = e E
and  E = ${\sigma  \over {{\varepsilon _0}}}$
$ 	herefore $   eVB = e $ 	imes $ ${\sigma  \over {{\varepsilon _0}}}$
$ \Rightarrow $   $\sigma $ = ${{\varepsilon _0}}$VB = $\sigma $
1
as   $\sigma $
1
= $-$ $\sigma $
2
$ 	herefore $   $\sigma $
2
= $-$ ${{\varepsilon _0}}$VB

Answer

$\sigma $
1
= $ \in $
0
$\upsilon $ B, $\sigma $
2
= $-$ $ \in $
0
$\upsilon $ B

Answer

$\sigma $
1
= ${{{ \in _0}\upsilon \,B} \over 2},$ $\sigma $
2
= ${{ - { \in _0}\,\upsilon B} \over 2}$

Answer

$\sigma $
1
= $\sigma $
2
= ${ \in _0}\,\upsilon B$

Answer

$\sigma $
1
= ${{ - { \in _0}\upsilon B} \over 2},$ $\sigma $
2
= ${{  { \in _0}\upsilon B} \over 2},$

Electromagnetic Induction

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