" PARAGRAPH 2
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 ⇁Bis applied on
the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the zdirection. 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."
Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are
w₁ and w₂ and thicknesses are d₁ and d₂, respectively. Two points K and M are symmetrically located on
the opposite faces parallel to the x-y plane (see figure). V₁ and V₂ 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)
(A) If w₁ = w₂ and d₁ = 2d₂, then V₂ = 2V₁ (B) If w₁ = w₂ and d₁ = 2d₂, then V₂ = V₁
(C) If w₁ = 2w₂ and d₁ = d₂, then V₂ = 2V₁ (D) If w₁ = 2w₂ and d₁ = d₂, then V₂ = V₁
Answers
Explanation:
(1), Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are and w2 and thicknesses are d1 and d2, respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V1 and V2 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)
(A) If w1=w2 and d1=2d2, then V2=2V1 (B) If w1=w2 and d1=2d2, then V2=V1
(C) If w1=2w2 and d1=d2, then V2=2V1 (D) If w1=2w2 and d1=d2, then V2=V1
(2), Consider two different metallic strips (1 and 2) of same dimensions (lengths ℓ , width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both along positive y-directions. Then V1 and V2 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)
(A) If B1=B2 and n1=2n2, then V2=2V1 (B) If B1=B2 and n1=2n2, then V2=V1
(C) If B1=2B2 and n1=n2, then V2=0.5V1 (D) If B1=2B2 and n1=n2, then V2=V1