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) :

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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