JEE Advanced 2015 · Paper 2 · Physics Q18

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PhysicsMultiple correct+4 / -2Question 18 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 same dimensions (length $l$ , width $w$ and thickness $d$ ) with carrier densities $n_1$ and $n_2$ , respectively. Strip 1 is placed in magnetic field $B_1$ and strip 2 is placed in magnetic field $B_2$ , both along positive $y$ -directions. Then $V_1$ and $V_2$ are the potential differences developed between $K$ and $M$ in strips 1 and 2, respectively. Assuming that the current $I$ is the same for both the strips, the correct option(s) is(are)

B_1=B_2

and

n_1=2n_2

, then

V_2=2V_1

B_1=B_2

and

n_1=2n_2

, then

V_2=V_1

B_1=2B_2

and

n_1=n_2

, then

V_2=0.5V_1

B_1=2B_2

and

n_1=n_2

, then

V_2=V_1

Answer and worked solution

Official answer: A, C

From $V=\dfrac{IB}{ned}$ , $V\propto\dfrac Bn$ .

(A) $n_1=2n_2$ gives $V_2=2V_1$ . True.
(C) $B_1=2B_2$ gives $V_2=0.5V_1$ . True.

(A), (C)

Topics:Force on a moving charge Drift velocity and current

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JEE Advanced 2015 · Paper 2, Physics question 18