A 100-turn coil has a radius of 7.50 cm and a resistance of 50.0 $\Omega$.At what rate must a perpendicular magnetic field change to produce a current of 5.00 A in the coil?
A)275 T/s
B)134 T/s
C)329 T/s
D)141 T/s
E)106 T/s

Question

Quizplus · Accepted Answer

The emf induced in a coil is given by

emf = -N(dΦ/dt)

where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux through the coil.

The magnetic flux through the coil can be calculated as

Φ = BA

where B is the magnetic field, and A is the area of the coil.

Since the magnetic field is perpendicular to the coil, the area A = πr^2, where r is the radius of the coil.

Using Ohm's law, the current in the coil is given by

I = emf/R

Combining all these equations, we get

I = -N(Bπr^2)/R(dt/dt)

Solving for dt/dt, we get

dt/dt = -IR/(Nπr^2B)

Plugging in the given values, we get

dt/dt = -(5.00 A)(50.0 Ω)/(100)(π)(0.0750 m)^2(B)

dt/dt = -6.62×10^-7B

To find the rate of change of magnetic field, we can rearrange the equation as

B = -dt/dt ÷ 6.62×10^-7

B = - (329 T/s) ÷ 6.62×10^-7

B = -4.97×10^8 T/s

The magnetic field cannot be negative, so we take the absolute value, giving

B = 4.97×10^8 T/s ≈ 329 T/s.

Therefore, the answer is (C) 329 T/s.

A 100-Turn Coil Has a Radius of 7 Ω\OmegaΩ At What Rate Must a Perpendicular Magnetic Field Change to a Resistance

A 100-Turn Coil Has a Radius of 7 $\Omega$ At What Rate Must a Perpendicular Magnetic Field Change to a Resistance