Marks: 2
The magnetic field of the loop increases from 0.0 Tesla to 0.2 Tesla in 0.4 seconds. The cross sectional area of the loop is 0.6 m2. What is the average current induced in the loop if the coil has a resistance of 1.5 Ω?
Choose one answer.
a. 0.1 A
b. 0.2 A
c. 0.4 A
d.0.6
To find the average current induced in the loop, we can use Faraday's law of electromagnetic induction, which states that the emf (electromotive force) induced in a loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through a loop is given by the product of the magnetic field (B) and the area (A) of the loop, i.e., φ = B * A.
Here, the magnetic field changes from 0.0 Tesla to 0.2 Tesla, and the cross-sectional area of the loop is 0.6 m^2.
The change in magnetic flux (Δφ) is therefore ΔB * A, where ΔB is the change in magnetic field (0.2 - 0.0) Tesla.
Since the change in magnetic field occurs over 0.4 seconds, we can calculate the average rate of change of magnetic flux (dφ/dt) as Δφ / Δt.
Finally, we can use Ohm's law (V = IR) to find the current (I) induced in the loop, where V is the emf induced and R is the resistance of the coil.
Putting it all together:
- The change in magnetic flux (Δφ) = (0.2 Tesla - 0.0 Tesla) * 0.6 m^2.
- The average rate of change of magnetic flux (dφ/dt) = Δφ / Δt = (0.2 T * 0.6 m^2) / 0.4 s.
- The emf induced (V) = dφ/dt by Faraday's law.
- The current (I) = V / R by Ohm's law.
Let's calculate the values:
Δφ = (0.2 T - 0.0 T) * 0.6 m^2 = 0.12 Wb (Webers).
dφ/dt = Δφ / Δt = (0.2 T * 0.6 m^2) / 0.4 s = 0.3 Wb/s (Webers per second).
Since the emf (V) induced is equal to the average rate of change of magnetic flux, V = dφ/dt = 0.3 Wb/s.
Finally, the current (I) induced in the loop can be found using Ohm's law:
I = V / R = 0.3 Wb/s / 1.5 Ω = 0.2 A.
Therefore, the average current induced in the loop is 0.2 A.
So, the correct answer is b. 0.2 A.