A circular coil enclosing an area of 89.5 cm2 is made of 140 turns of copper wire as shown in the figure.

Question

A circular coil enclosing an area of 89.5 cm2 is made of 140 turns of copper wire as shown in the figure. When viewed from the right the coil is wound counter-clockwise. A 7.6 Ω resistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 2.32 T points horizontally from left-to-right through the perpendicular plane of the coil.

During a 6.1 minute time interval the field uniformly changes at a constant rate, until a reversed field is reached equal in magnitude to the initial field. How much charge flows through the coil? Answer in units of C.

Answer 1

The area of the coil in meter squared is 0.00895 m²

The effective area is 140 times that = 1.253 m²

The total time for the field to change direction is 366 s and the field changes by 4.64 T since it now goes in the opposite direction

using ε=-ΔΦ/Δt we get 1.253 x 4.64/366 = 0.0159 V

Since the current is given by V/R we get 0.0159/7.6 = 0.00209 A

As current is defined as charge over time, the total charge is 0.00209 x 366 = 0.6396 C