A conducting square loop of side L , mass M and resistance R is moving in the X Y plane with its edges parallel to the X and Y axes. The region y 0 has a uniform magnetic field, B =B₀ k . The magnetic field is zero everywhere else. At time t=0 , the loop starts to enter the magnetic field with an initial velocity v₀ ~m / s , as shown in the figure. Considering the quantity K= B₀^2 L^2 R M in appropriate units, ignori

Step-by-step solution

- d dt = d dt ( B ₀ y )= BV aligned & F = B ( i )( )(- j ) & ma =- B ₀ [ ~B ₀ ~V R ]( ) & a =- B ₀^2 ^2 ~V mR aligned aligned & Also K= B₀^2 ^2 V R M & So [a=-k v] & d v d t =-k v & _ v₀ ^v d v d t = ₀^t-k d t & n v v₀ =-k t aligned [ v = v ₀ e ^ - kt ] [ v = v ₀ e ^ - kt ] .( i ) dx dt = v ₀ e ^ - kt ( x ) aligned & ₀^ x dx = ₀^ t v ₀ e ^ - kt dt & = v ₀ k (1- e ^ - kt ) aligned When x= = V ₀ k (1- e ^ - kt ) Option (D) ( v ₀=3 k ) aligned & = 3 k k (1- e ^ - kt ) & 1 3 =1- e ^ - kt & f 2 3 =2 e ^ - kt & - kt =8 n