JEE Advanced 2015 · Paper 2 · Physics Q17

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PhysicsMultiple correct+4 / -2Question 17 of 60

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In a thin rectangular metallic strip a constant current $I$ flows along the positive $x$ -direction, as shown in the figure. The length, width and thickness of the strip are $l$ , $w$ and $d$ , respectively. A uniform magnetic field $\vec B$ is applied on the strip along the positive $y$ -direction. Due to this, the charge carriers experience a net deflection along the $z$ -direction. This results in accumulation of charge carriers on the surface $PQRS$ and appearance of equal and opposite charges on the face opposite to $PQRS$ . A potential difference along the $z$ -direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

A flat metallic strip of length l along x, width w along z and thickness d along y, carrying current I in the +x direction. The near face PQRS (in the x-y plane, facing +z) carries point M; the opposite face carries point K. Axes: x right, y up, z out of the page.

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are $w_1$ and $w_2$ and thicknesses are $d_1$ and $d_2$ , respectively. Two points $K$ and $M$ are symmetrically located on the opposite faces parallel to the $x$ - $y$ plane (see figure). $V_1$ and $V_2$ are the potential differences between $K$ and $M$ in strips 1 and 2, respectively. Then, for a given current $I$ flowing through them in a given magnetic field strength $B$ , the correct statement(s) is(are)

w_1=w_2

and

d_1=2d_2

, then

V_2=2V_1

w_1=w_2

and

d_1=2d_2

, then

V_2=V_1

w_1=2w_2

and

d_1=d_2

, then

V_2=2V_1

w_1=2w_2

and

d_1=d_2

, then

V_2=V_1

Answer and worked solution

Official answer: A, D

Hall voltage. In equilibrium $eE=evB$ , so the voltage across the width is $V=Bvw$ . With $I=nevwd$ :
$V=\frac{IB}{ned}.$
It depends on the thickness $d$ but not on the width $w$ .

(A) $d_1=2d_2$ gives $V_2=2V_1$ . True.
(D) $w_1=2w_2$ with equal $d$ gives $V_2=V_1$ . True.

(A), (D)

Topics:Force on a moving charge Drift velocity and current

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JEE Advanced 2015 · Paper 2, Physics question 17