Faraday's law with loop of wire and resistor

In summary, a coil with a 3.65 cm radius and 560 turns is placed in a varying magnetic field with a time-dependent equation. The coil is connected to a resistor and its plane is perpendicular to the magnetic field. At time t0 = 4.50 s, the current in the resistor can be calculated by multiplying the induced emf value by the number of turns and dividing by the resistance. The induced emf value can be found using the equation E= 2.81×10^−2 V +( 2.86×10^−4 V/s3 )t^3. It may also be necessary to include the factor E = - L di / dt, depending on whether the concept of self
  • #1
xSpartanCx
18
0
A coil 3.65 cm radius, containing 560 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10^−2 T/s)t+( 3.05×10^−5 T/s4)t^4. The coil is connected to a 600-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.
What is the current in the resistor at time t0 = 4.50 s ?I got the correct induced emf value:
E= 2.81×10^−2 V +( 2.86×10^−4 V/s3 )t^3

I've tried plugging in 4.5s into the emf equation and then dividing I = V/R but the answer is incorrect.
 
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  • #2
xSpartanCx said:
I got the correct induced emf value:
E= 2.81×10^−2 V +( 2.86×10^−4 V/s3 )t^3
Did you multiply it by the no of turns(560)?
 
  • #3
cnh1995 said:
Did you multiply it by the no of turns(560)?
Yes, that's part of the emf value.
 
  • #4
Has your course covered self-inductance?
Perhaps you're expected to include the factor E = - L di / dt.
 

1. What is Faraday's law with a loop of wire and resistor?

Faraday's law states that when there is a change in magnetic flux through a closed loop of wire, an electromotive force (EMF) is induced in the loop. This EMF can cause a current to flow in the loop if there is a complete circuit, such as when a resistor is connected.

2. How does the loop of wire and resistor affect Faraday's law?

The loop of wire and resistor act as a closed circuit for the induced EMF to flow through. The resistor also creates a resistance to the current, causing it to dissipate energy in the form of heat.

3. What is the relationship between the change in magnetic flux and the induced EMF?

According to Faraday's law, the induced EMF is directly proportional to the rate of change of magnetic flux through the loop of wire. This means that a larger change in magnetic flux will result in a larger induced EMF.

4. Can Faraday's law be used to generate electricity?

Yes, Faraday's law is the basis for electromagnetic induction, which is used in many devices to convert mechanical energy into electrical energy. For example, generators use Faraday's law to produce electricity by rotating a loop of wire in a magnetic field.

5. What factors can affect the magnitude of the induced EMF in Faraday's law?

The magnitude of the induced EMF is affected by the rate of change of magnetic flux, the number of turns in the loop of wire, and the strength of the magnetic field. Additionally, the presence of a resistor in the circuit can also affect the magnitude of the induced EMF.

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