A planar loop consisting of 4 turns of wire, each of which encloses 200 cm2, is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 5.0 $\Omega$ ?

Question

A planar loop consisting of 4 turns of wire, each of which encloses 200 cm2, is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 5.0  $\Omega$ ?

Quizplus · Accepted Answer

The induced emf in the loop is given by Faraday's law:
emf = -N(dΦ/dt) 
where N is the number of turns, Φ is the magnetic flux through one turn, and t is time.

Initially, the magnetic field is 10 mT, so the magnetic flux through one turn is:
Φ = BA = (10×10^-3 T)(200×10^-4 m^2) = 2×10^-3 Wb.

At the final time, the magnetic field is 25 mT, so the magnetic flux through one turn is:
Φ = BA = (25×10^-3 T)(200×10^-4 m^2) = 5×10^-3 Wb.

The change in magnetic flux over the time interval is therefore:
ΔΦ = 5×10^-3 Wb - 2×10^-3 Wb = 3×10^-3 Wb.

The time interval is given as 5.0 ms, so we have:
Δt = 5.0×10^-3 s.

Now we can find the induced emf:
emf = -N(dΦ/dt) = -(4)(3×10^-3 Wb / 5.0×10^-3 s) = -2.4 V.

Finally, we can use Ohm's law to find the induced current:
I = emf / R = (2.4 V) / (5.0 Ω) = 0.48 A = 480 mA.

Therefore, the answer is (D) 48 mA.

A Planar Loop Consisting of 4 Turns of Wire, Each Ω\OmegaΩ

A Planar Loop Consisting of 4 Turns of Wire, Each $\Omega$