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^-2T to 13.0 x 10^-2 Tin 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 ohms. Find the induced current I.

Answer 1

2.93 x 10⁻⁴ volts

4.88 x 10⁻⁵ A

Step-by-step explanation:

N = Number of turns in cylindrical coil = 400

r = radius of the coil = 2 cm = 0.02 m

Area of the coil is given as

A = πr²

A = (3.14)(0.02)²

A = 12.56 x 10⁻⁴ m²

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

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

Induced emf is given as

`E=(NA\Delta B)/(t)`

`E=((400)(12.56* 10^(-4))(0.07))/(120)`

E = 2.93 x 10⁻⁴ volts

R = resistance of the resistor = 6 ohm

i = induced current

Using ohm's law

E = i R

2.93 x 10⁻⁴ = i (6)

i = 4.88 x 10⁻⁵ A