A rectangular metallic block has dimensions 5 cm, 10 cm, and 15 cm along the x , y , and z axes respectively. It is moving with a velocity v = (2 i + 3 j ) m/s in a region of uniform magnetic field B = ( j + 2 k ) T. The maximum potential difference developed between any two opposite faces of the block is V mV. The value of V is

Step-by-step solution

The induced electric field inside the moving metallic block is given by E = v B . Substituting the given vectors: E = (2 i + 3 j ) ( j + 2 k ) Calculating the cross product: E = 2( i j ) + 4( i k ) + 3( j j ) + 6( j k ) E = 2 k - 4 j + 0 + 6 i = (6 i - 4 j + 2 k ) V/m. The potential difference between opposite faces perpendicular to a given axis is the product of the magnitude of the electric field component along that axis and the length of the block along that axis ( V = E_d d ). For faces perpendicular to the x