A metal strip 575 cm long 0870 cm wide and 0957 mm thick mov

A metal strip 5.75 cm long, 0.870 cm wide, and 0.957 mm thick moves with constant velocity through a uniform magnetic field B = 0.980 mT directed perpendicular to the strip, as shown in the figure. A potential difference of 5.49 µV is measured between points x and y across the strip. Calculate the speed v. Show all work.

Solution

For any charge between x and y inside the metal strip two forces will be acting upon it. One will be the force due to the electric field between x and y and other will be due to its motion in the magnetic field.

Now for equilibrium to be achieved, the net force on the charge must be zero.

So we can write: F = qE + qVB = 0

or, v = -E/B

Also, we know that E is given as E = -dv/dx where v is the potential change between the two points. In the given situation, we already know the potential difference and distance between the points, hence we can find the electric field as: E = (V1 - V2) / width = 5.49 x 10^-6 / 0.87 x 10^-2

Using this in the above equation for the velocity we get:

V = 5.49 x 10^-6 /0.98 x 10^-3 x 0.87 x 10^-2 = 0.6439 m/s

Therefore the required speed is 0.6439 m/s