Question

Which of the following correctly compares the field inside a toroid with the field inside a solenoid?

Options

• Both have \(B = \frac{\mu_0 nI}{2}\) since both are long coils

• Both have \(B = 0\) inside since fields cancel in closed windings

• Solenoid: \(B = \frac{\mu_0 N I}{2\pi r}\); Toroid: \(B = \mu_0 nI\)

• Solenoid: \(B = \mu_0 nI\) (uniform); Toroid: \(B = \frac{\mu_0 N I}{2\pi r}\) (varies with \(r\))

Answer 1

Inside a solenoid, the field is \(B = \mu_0 nI\), which is uniform. Inside a toroid, the field is \(B = \frac{\mu_0 N I}{2\pi r}\), which varies with the radial distance \(r\) from the center. Thus the solenoid's interior field is uniform while the toroid's is not uniform and depends on radius.