# Faraday's Law and magnetic field

• erik-the-red
In summary, the induced emf in the coil as a function of time can be expressed as n*pi*r^2(A+4Bt^3), where n is the number of turns, r is the radius of the coil, A is the constant in the magnetic field equation, and B is the coefficient of the time term. The negative sign is usually neglected unless coordinates are defined properly.
erik-the-red
A coil containing N = 550 turns with radius r = 3.90 cm, is placed in a uniform magnetic field that varies with time according to $$B=(At + Bt^4)$$, where $$A = 1.05 \cdot 10^−2 {\rm T}/{\rm s}$$ and $$B = 3.00 \cdot 10^−5 {\rm T}/{\rm s}^{4}$$. The coil is connected to a resistor of resistance 640 Ohms, and its plane is perpendicular to the magnetic field. The resistance of the coil can be neglected.

Find the magnitude of the induced emf in the coil as a function of time. Write your answer as an expression in terms of the variables given in the problem.

I'm thinking that the derivative of magnetic flux can be written as the derivative of (BA). A is constant, so it's A multiplied by the derivative of B.

I get $$(A + 4Bt^3)(A)$$.

The induced EMF is the negative of that multiplied by N.

I typed that in, but it wasn't right.

What did I not consider?

Last edited:
the derivative of the flux with respect to time is going to be

n(area) (d B/dt)

or n*pi*r^2(A+4Bt^3)

I usually neglect the negative sign unless the problem allows you to define coordinates properly.

I see I did not use the radius for the area.

Thank you.

## 1. What is Faraday's Law and how does it relate to magnetic fields?

Faraday's Law is a fundamental principle in electromagnetism that describes the relationship between a changing magnetic field and the induced electric field. It states that when a magnetic field changes in intensity or direction, it will induce an electric field in any nearby conductor.

## 2. How does Faraday's Law apply to generators and motors?

In generators, Faraday's Law is used to convert mechanical energy into electrical energy by rotating a coil of wire in a magnetic field. The changing magnetic field induces an electric current in the wire, which can then be used as a source of power. In motors, the opposite is true, where an electric current is used to create a magnetic field, which then causes the motor to rotate.

## 3. What is the difference between Faraday's Law and Lenz's Law?

Faraday's Law and Lenz's Law are both principles that describe the relationship between changing magnetic fields and induced electric fields. However, while Faraday's Law states that a changing magnetic field will induce an electric field, Lenz's Law states that the induced electric field will always oppose the change in the magnetic field that caused it.

## 4. How is Faraday's Law used in everyday life?

Faraday's Law has many practical applications in everyday life. It is used in power plants to generate electricity, in electric motors and generators, and in devices such as transformers and electric motors. It is also used in technologies like MRI machines and electrical transformers.

## 5. Can Faraday's Law be used to explain electromagnetic induction in reverse?

Yes, Faraday's Law can also be used to explain electromagnetic induction in reverse, known as the motional electromotive force. This occurs when a conductor moves through a magnetic field, causing a change in the magnetic flux and inducing an electric field. This is the principle behind devices such as electric generators and bicycle dynamos.

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