The figure shows a metallic block with its faces parallel to

The figure shows a metallic block, with its faces parallel to coordinate axes. The block is in a uniform magnetic field of magnitude 0.017 T. One edge length of the block is 24 cm; the block is not drawn to scale. The block is moved at 2.2 m/s parallel to each axis, in turn, and the resulting potential difference V that appears across the block is measured. With the motion parallel to the y axis, V =17 mV; with the motion parallel to the z axis, V = 13 mV; with the motion parallel to the x axis, V = 0. What are the block lengths (a) d_x, (b) d_y, and (c) d_z?

Solution

Since d=V/E =V/vB

a)

d_x=24 cm

b)

d_y = 17*10^-3/2.2*0.017

d_y=0.4545 =45.45 cm

c)

d_z = 13*10^-3/2.2*0.017

d_z=0.3476 m =34.76 cm