a metallic block, with its faces parallel to coordinate axes. The block is in a

Question

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 22 cm; the block is not drawn to scale. The block is moved at 2.3 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 = 12 mV; with the motion parallel to the x axis, V = 0. What are the block lengths (a) dx, (b) dy, and (c) dz?

Explanation / Answer

Given that the magnitude of magnetic field is B = 0.017 T Length of the block is L = 22 cm = 0.22m The speed of the block is v = 2.3 m/s ------------------------------------------------------------------------------ The potential difference between ends of conductor that is moving with velocity v is V = Bdv (a) The edge length dx = 22 cm (b)If the the motion parallel to the z axis, induced voltage V = 12 mV Then dy = V / Bv = 12 mV / 0.017 T*2.3 m/s = 0.3069 m =30.69 cm (c) If the motion parallel to the y axis, V =17 mV Then dz = V / Bv = 17 mV / 0.017 T*2.3 m/s = 0.4347 m =43.47 cm (b)If the the motion parallel to the z axis, induced voltage V = 12 mV Then dy = V / Bv = 12 mV / 0.017 T*2.3 m/s = 0.3069 m =30.69 cm (c) If the motion parallel to the y axis, V =17 mV Then dz = V / Bv = 17 mV / 0.017 T*2.3 m/s = 0.4347 m =43.47 cm Then dy = V / Bv = 12 mV / 0.017 T*2.3 m/s = 0.3069 m =30.69 cm (c) If the motion parallel to the y axis, V =17 mV Then dz = V / Bv = 17 mV / 0.017 T*2.3 m/s = 0.4347 m =43.47 cm Then dy = V / Bv = 12 mV / 0.017 T*2.3 m/s = 0.3069 m =30.69 cm (c) If the motion parallel to the y axis, V =17 mV Then dz = V / Bv = 17 mV / 0.017 T*2.3 m/s = 0.4347 m =43.47 cm Then dz = V / Bv = 17 mV / 0.017 T*2.3 m/s = 0.4347 m =43.47 cm

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