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Q.

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(see figure).If charge densities σ1   and   σ2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects):

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a

σ1=−ε0vB2,σ2=ε0vB2

b

σ1=ε0vB,   σ2=−ε0vB

c

σ1=ε0vB2,  σ2=−ε0vB2

d

σ1=σ2=ε0vB

answer is B.

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Detailed Solution

∵F=qE and F=qvB ∴E=vB  And Gauss's law in Electrostatic E=σε0 E=σε0=vB⇒σ=ε0vB σ1=−σ2
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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(see figure).If charge densities σ1   and   σ2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects):