# Magnetic field and induced EMF

#### jaymode

Here is the problem:
A coil containing 590 turns with radius 3.85 cm, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T\s)t+( 3.40×10−5 T\s^4)t^4. The coil is connected to a resistor of resistance 690 Ohms, and its plane is perpendicular to the magnetic field. The resistance of the coil can be neglected.

A)Find the magnitude of the induced emf in the coil as a function of time.
I found that by taking the derivative of B and multiplying that by the number of turns time the area and got:
2.75*(0.012+(0.000102*(t^3))) V

which Mastering Physics tells me is right.

B)What is the current in the resistor at time t_0 = 5.00 s?
I tried to solve this by using the equation from A and plugging in 5 for t. Then I divided that by the resistance which is 690 ohms.

The answer I got was 9.8641*10^-5, however Mastering Physics tells me it wrong.

Where am I going wrong?

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#### Andrew Mason

Homework Helper
jaymode said:
A)Find the magnitude of the induced emf in the coil as a function of time.
I found that by taking the derivative of B and multiplying that by the number of turns time the area and got:
2.75*(0.012+(0.000102*(t^3))) V

which Mastering Physics tells me is right.

B)What is the current in the resistor at time t_0 = 5.00 s?
I tried to solve this by using the equation from A and plugging in 5 for t. Then I divided that by the resistance which is 690 ohms.

The answer I got was 9.8641*10^-5, however Mastering Physics tells me it wrong.

Where am I going wrong?
Since the resistor is in series with the coil, the current through the resistor is the solution to this differential equation:

$$V = L\frac{dI}{dt} + IR$$

where V is the induced emf that you found in a).

So I think you need to solve this differential equation.

AM

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