Question

The magnetic field through a 16 cm diameter loop increases from 1.10 T into the page to 2.10 T out of the page in 0.15 s. The resistance of the loop is 0.10 ohms. Find the magnitude and direction of the current in the loop

Answer 1

Answer 2

To find the magnitude and direction of the current in the loop, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a loop is equal to the rate of change of magnetic flux through the loop.

The formula for the induced EMF is given by:

EMF = -N * ΔΦ/Δt

Where:

• EMF is the induced electromotive force

• N is the number of turns in the loop

• ΔΦ is the change in magnetic flux

• Δt is the change in time

Given information:

• Diameter of the loop: 16 cm

• Radius of the loop: r = 8 cm = 0.08 m

• Initial magnetic field: B1 = 1.10 T (into the page)

• Final magnetic field: B2 = 2.10 T (out of the page)

• Time interval: Δt = 0.15 s

• Resistance of the loop: R = 0.10 Ω

Step 1: Calculate the change in magnetic flux (ΔΦ): The change in magnetic flux is given by the product of the area of the loop (A) and the change in magnetic field (ΔB):

ΔΦ = A * ΔB

Since the loop is a circle, the area is given by A = π * r^2:

ΔΦ = π * r^2 * (B2 - B1)

Step 2: Calculate the number of turns in the loop (N): The number of turns is not given in the problem statement. If we assume a single-turn loop, N = 1.

Step 3: Calculate the induced EMF (EMF): Using the formula for EMF and substituting the known values:

EMF = -N * ΔΦ/Δt = -(1) * (π * r^2 * (B2 - B1))/Δt

Step 4: Calculate the current (I): The current in the loop can be calculated using Ohm's Law:

EMF = I * R

Rearranging the equation:

I = EMF / R

Substituting the value of EMF and R:

I = [-(1) * (π * r^2 * (B2 - B1))/Δt] / R

Finally, we can plug in the given values to find the magnitude and direction of the current in the loop.

Note: The negative sign in the formula indicates the direction of the induced current