Question

Using a coil made of 219 turns of single‑strand copper wire, you use a motor to rotate the coil at a constant angular speed of 90.0 rev/s at various orientations and locations throughout the room. In one particularly significant orientation, you notice a maximum induced voltage of 1.15 V appearing in the coil.
If the radius of the coil is 1.00 cm, how strong was the magnetic field that produced this emf?

Answer 1

Answer:

0.0222T

Explanation:

Frequency (f) =90 rev/s

Voltage = 1.15 v

Radius of coil = 1.00cm

= 0.01m

No of turns of wire (N) = 291

ω = 2πf

ω = 2π(90)

ω = 180π

A(t)= πr².sin ωt

= π(0.01)². Sin180πt

= 0.0001π.sin180πt

Differentiate A(t) with respect to t

dA/dt = 0.0001π . 180π . cos 180πt

EMF = - NB(dA/dt)

B = EMF/N(dA/dt)

B = 1.15/ -291(0.0001π . 180π . cos 180πt)

At the moment of induced voltage, cos180π = 1

B = 1.15/ -291(0.0001π . 180π . 1)

B = 1.15/ -51.7

B = 0.0222 T

The strength of the magnetic field = 0.0222T