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?

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Physics

16 December, 22:08

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?

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Fifi · Answer 1

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