As shown in the figure, a conducting disc rotates about its axis within a perpendicular magnetic field B . A resistor having resistance R is linked between the centre and the rim. Evaluate the current passing through the resistor and determine if it enters or leaves the disc at the centre. The radius of the disc is 5.0 cm , its angular speed = 10 rad/s , B = 0.40 T , and R = 10 .

Step-by-step solution

The induced emf E between the centre and the rim of a rotating conducting disc in a uniform magnetic field is given by: E = 1 2 B r^2 Given values are: B = 0.40 T = 10 rad/s r = 5.0 cm = 0.05 m Substituting these values into the formula: E = 1 2 0.40 10 (0.05)^2 E = 2.0 0.0025 = 0.005 V The current I passing through the resistor R = 10 is: I = E R = 0.005 10 = 0.0005 A = 0.5 mA To determine the direction of the current, we use the Lorentz force on a positive charge q inside the disc, which is F = q( v B ) . The mag