JEE Main 2016 · 10 Apr · Shift 1 · Physics Q15

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PhysicsSingle correct+4 / -1Question 15 of 90

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) :

A thin vertical metal sheet moving up with speed v in a magnetic field B into the page; its left face carries σ₁ and its right face σ₂.

\sigma_1=\epsilon_0vB

\sigma_2=-\epsilon_0vB

\sigma_1=\dfrac{\epsilon_0vB}2

\sigma_2=\dfrac{-\epsilon_0vB}2

\sigma_1=\sigma_2=\epsilon_0vB

\sigma_1=\dfrac{-\epsilon_0vB}2

\sigma_2=\dfrac{\epsilon_0vB}2

Answer and worked solution

Official answer: A

The free charges feel $q\vec v\times\vec B$ ; with $\vec v$ up and $\vec B$ into the page this pushes positive charge to the left face. In equilibrium the field between the faces cancels $vB$ : $\frac\sigma{\epsilon_0}=vB$ . So $\sigma_1=\epsilon_0vB$ and $\sigma_2=-\epsilon_0vB$ .

Topics:Motional EMF Conductors and charge distribution

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JEE Main 2016 · 10 Apr · Shift 1, Physics question 15