A closed circular coil (with both ends joined together) of radius 2.00 cm comprises 50 turns and possesses a resistance of 4.00 . A uniform magnetic field B = 0.200 T is present in the region, directed parallel to the axis of the loop. The coil is then rotated about a diameter by an angle of 60.0^ in a time of 0.100 s . Calculate the net charge crossing a cross-section of the wire of the coil.

Step-by-step solution

The net charge flowing through a circuit is given by Q = R , where is the change in magnetic flux and R is the resistance. Initial magnetic flux through the coil is _i = N B A (0^ ) = N B ( r^2) . Final magnetic flux after rotating by 60^ is _f = N B A (60^ ) = 1 2 N B ( r^2) . The magnitude of change in flux is: = _i - _f = 1 2 N B r^2 Substituting the given values: = 1 2 50 0.200 (0.02)^2 = 5 4 10⁻⁴ = 2 10⁻³ Wb The net charge crossing the cross-section is: Q = R = 2 10⁻³ 4.00 = 0.5 10⁻³ C Q 0.5 3.14 10⁻³ C = 1.57