PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity `vec(v)` from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left.

For `x = a//4`
(i) magnetic flux through the loop,
(ii) induced current in the loop and
(iii) external force required to maintain constant velocity of the loop, will be

Options

A. (i) `Ba^(2)` (ii) `(Bav)/(2R)` (iii) `(B^(2)a^(2)v^(2))/(4R^(2))`
B. (i) `Ba^(2)` (ii) zero (iii) zero
C. (i) `Ba^(2)` (ii) `(Bav)/(2R)` (iii) zero
D. (i) zero (ii) zero (iii) zero

Answer

C

Explanation

At `x=-(a)/(4)`, loop is completely inside the field. Flux through the loop is `BA=Ba^(2)`. As (dB)/(dt)=0`, induced current is zero so is external force is required.