# Solve Emf & Current for Changing Magnetic Field in Square Coil

• buckeyes
In summary, a changing magnetic field induces an emf of 0.76V and a current of 3.1A in a single-turn circular coil. When the coil is re-formed into a single-turn square coil, the same changing magnetic field induces an emf of 0.589V, but the current induced is unknown. By using Ohm's Law and knowing the resistance of the coil, you can find the current induced, which is 2.40A.
buckeyes

## Homework Statement

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.76 V and a current of 3.1 A are induced in the coil. The wire is the re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What emf and current are induced in the square coil?

I=ER

## The Attempt at a Solution

i found the emf (.589V) but i can't figure out the current. what do i do?

Well your equation is wrong, it's Ohm's Law, remember

So if you know the voltage and current, you can find the resistance of the coil, which doesn't change. Therefore if you change the voltage(which you've done by reshaping the coil), you can find the current induced

2.40a?

## 1. How do you calculate the induced EMF in a square coil with a changing magnetic field?

To calculate the induced EMF in a square coil with a changing magnetic field, you can use the formula EMF = -N*dΦ/dt, where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux through the coil. This formula is known as Faraday's law of electromagnetic induction.

## 2. What is the relationship between EMF and current in a changing magnetic field?

In a changing magnetic field, the induced EMF will cause a current to flow through the coil. The magnitude of the current is directly proportional to the magnitude of the induced EMF. This relationship is described by Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R), or I = V/R.

## 3. How does the shape of the coil affect the induced EMF and current?

The shape of the coil can affect the induced EMF and current in a changing magnetic field. For a given magnetic field, a coil with more turns will have a larger induced EMF and current compared to a coil with fewer turns. Additionally, a coil with a larger area will have a higher induced EMF and current compared to a coil with a smaller area.

## 4. Can the direction of the induced current be determined in a square coil?

Yes, the direction of the induced current in a square coil can be determined using Lenz's law. This law states that the induced current will flow in a direction that opposes the change in magnetic flux that caused it. In a square coil, the direction of the induced current will depend on the direction of the changing magnetic field and the orientation of the coil.

## 5. How can the induced EMF and current be increased in a changing magnetic field?

The induced EMF and current can be increased in a changing magnetic field by increasing the strength of the magnetic field, increasing the number of turns in the coil, or increasing the rate of change of the magnetic field. Additionally, using a ferromagnetic core inside the coil can also increase the induced EMF and current by concentrating the magnetic field within the coil.

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