Why Does Changing Magnetic Field Direction Affect Current in a Wire Loop?

[Destrio]

Homework Statement

A loop of wire of aream 0.32m^2 is palced in a 0.75 T magnetic field. The magnetic field is changed to 0.35 T in the opposite direction in 0.45 s . What is the magnitude of the current through the 15 ohm resistor.

Homework Equations

emf = -N (flux / time)

The Attempt at a Solution

emf = (-1) [(.35T)(.32m^2)-(.75T)(.32m^2)]/(.45s)
emf = .284 V
V = IR
I = .284 V / 15ohm
I = .019 A

.019 is the wrong answer in the multiple choice
the correct answer is supposed to be 0.052 A

Thanks

 

[OlderDan]

Homework Statement

A loop of wire of aream 0.32m^2 is palced in a 0.75 T magnetic field. The magnetic field is changed to 0.35 T in the opposite direction in 0.45 s . What is the magnitude of the current through the 15 ohm resistor.

Homework Equations

emf = -N (flux / time)

The Attempt at a Solution

emf = (-1) [(.35T)(.32m^2)-(.75T)(.32m^2)]/(.45s)
emf = .284 V
V = IR
I = .284 V / 15ohm
I = .019 A

.019 is the wrong answer in the multiple choice
the correct answer is supposed to be 0.052 A

Thanks

Looks like you have not computed the change in field correctly.

 

[m2003]

for providing the question and your attempt at a solution. It seems like you have made a mistake in calculating the emf (electromotive force) in your solution. The correct equation for calculating emf is emf = -N(dΦ/dt), where N is the number of turns in the loop and dΦ/dt is the rate of change of magnetic flux through the loop. In this case, N = 1 and dΦ/dt = (ΔBΔA)/Δt = ((0.35T - 0.75T)(0.32m^2))/0.45s = -0.177 Tm^2/s. Plugging these values into the equation, we get emf = -(-0.177 Tm^2/s) = 0.177 V.

Now, using Ohm's law, we can calculate the current through the resistor as I = V/R = 0.177 V / 15 ohm = 0.0118 A. However, this is the current at the instant the magnetic field changes from 0.75 T to 0.35 T. To find the average current over the entire 0.45 seconds, we need to use the average emf, which is half of the initial and final emf (since the change in magnetic field is linear). So, the average emf is (0.177 V + 0 V)/2 = 0.0885 V. Using this value in Ohm's law, we get the average current as I = 0.0885 V / 15 ohm = 0.0059 A.

Therefore, the correct answer is 0.0059 A or 0.006 A (depending on the level of precision required). I hope this helps to clarify the solution for you. Keep up the good work!