A coil consists of 200turns of wire . Each turns is a square of side d=18cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50T in 0.80s, what is the magnitude of the induced emf in the coil while the field is changing and find the magnitude of the induced current in the coil while the field is changing

Question

A coil consists of 200turns of wire . Each turns is a square of side d=18cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50T in 0.80s, what is the magnitude of the induced emf in the coil while the field is changing and find the magnitude of the induced current in the coil while the field is changing

Answer 1

To find the magnitude of the induced emf in the coil while the field is changing, we can use Faraday's law of electromagnetic induction:

emf = -N * (ΔΦ/Δt)

Where:
emf is the induced electromotive force (emf)
N is the number of turns in the coil (200 turns)
ΔΦ is the change in magnetic flux
Δt is the change in time

First, let's find the change in magnetic flux.
The magnetic flux (Φ) through a loop of wire is given by:

Φ = B * A

Where:
Φ is the magnetic flux
B is the magnetic field strength
A is the area of the loop

Since each turn of the coil is a square of side d = 18cm, the area of each turn is A = d^2 = (0.18m)^2 = 0.0324 m^2.

Next, let's find the change in time, Δt = 0.80s.

Now, let's find the change in magnetic field, ΔB.
ΔB = B_final - B_initial = 0.50T - 0T = 0.50T.

Now we can substitute these values into the emf equation:
emf = -200 * (ΔΦ/Δt) = -200 * ((B_final * A - B_initial * A) / Δt)
emf = -200 * ((0.50T * 0.0324 m^2 - 0T * 0.0324 m^2) / 0.80s)

Calculating this expression, we find that the magnitude of the induced emf in the coil while the field is changing is approximately 40V.

To find the magnitude of the induced current in the coil while the field is changing, we can use Ohm's law:

emf = I * R

Where:
emf is the induced electromotive force (emf)
I is the induced current
R is the resistance

Since the coil is made of wire and the resistance is not given in the problem, we'll assume a hypothetical resistance value for the coil.

Let's say the resistance of the coil is R = 10Ω.

Now we can substitute the values into Ohm's law to find the induced current:
emf = I * R
40V = I * 10Ω

Solving for I, we find that the magnitude of the induced current in the coil while the field is changing is 4A.