Question

A cylindrical coil has 400 turns and a radius of 2.00 cm. The external magnetic field in the region of the coil is uniform and axial. The field rises from 6.00 x 10^-2 T to 13.0 x 10^-2 T in 2.00 minutes. Find the induced emf across the ends of the coil. The ends of the coil are attached to a resistor of 6.00 ohms. Find the induced current I.

Answer 1

Answer:

2.93 x 10⁻⁴ Volts

Explanation:

N = number of turns in the cylindrical coil = 400

r = radius = 2 cm = 0.02 m

A = Area = πr² = (3.14) (0.02)² = 0.001256 m²

ΔB = Change in magnetic field = 0.13 - 0.06 = 0.07 T

t = time interval = 2 min = 2 x 60 s = 120 s

R = resistance of the resistor = 6 Ω

Induced emf between the ends of coil is given as

$E = \frac{N\Delta BA}{t}$

$E = \frac{(400)(0.07)(0.001256)}{120}$

E = 2.93 x 10⁻⁴ Volts