Electric field induced in a ring

[hapax]

Homework Statement

A metal ring 4.6 cm. in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.260 T/s.

a.) What is the magnitude of the electric field induced in the ring?

Homework Equations

Flux = BA
Induced EMF = -dFlux/dt


The change in magnetic field, it seems, should be affecting the magnetic flux through the ring and thus inducing a counter-clockwise current. I thought that this change in flux could be expressed by (.260 T/s)*(2(pi)(4.6cm/2)^2) or the change in magnetic field times the area, but this is wrong. I don't really know where to begin, any help would be appreciated.

 

[kamerling]

Homework Statement

A metal ring 4.6 cm. in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.260 T/s.

a.) What is the magnitude of the electric field induced in the ring?

Homework Equations

Flux = BA
Induced EMF = -dFlux/dt


The change in magnetic field, it seems, should be affecting the magnetic flux through the ring and thus inducing a counter-clockwise current. I thought that this change in flux could be expressed by (.260 T/s)*(2(pi)(4.6cm/2)^2) or the change in magnetic field times the area, but this is wrong. I don't really know where to begin, any help would be appreciated.

I think you got the area wrong. 4.6 cm is the diameter and not the radius. You also need the area in m^2

 

[Moetasim]

I would begin by first understanding the concept of electromagnetic induction. When a conductor, such as the metal ring in this scenario, moves through a changing magnetic field, an electric field is induced in the conductor. This is known as Faraday's Law of Induction. The induced electric field is a result of the changing magnetic flux through the ring.

In this case, the magnetic field is decreasing at a constant rate of 0.260 T/s. This means that the change in magnetic flux through the ring is also changing at this rate. We can calculate the change in magnetic flux by multiplying the change in magnetic field by the area of the ring, as you have correctly stated.

However, there are a few things to consider. First, the area of the ring should be expressed in square meters, not square centimeters. So we need to convert the diameter of the ring from centimeters to meters. Secondly, the magnetic flux is a vector quantity, so we need to consider the direction of the magnetic field and the orientation of the ring.

Assuming the ring is placed perpendicular to the magnetic field, the magnetic flux will be maximum when the ring is in the initial position (between the magnets) and will decrease as the magnets are pulled apart. This means that the induced electric field will also be changing in magnitude and direction.

To calculate the magnitude of the induced electric field, we can use the equation:

E = -d(Φ)/dt

Where E is the electric field, Φ is the magnetic flux, and t is time.

Substituting the values given in the problem, we get:

E = -(0.260 T/s)(π(0.023 m)^2) = -9.65 x 10^-5 V/m

This means that the induced electric field in the ring is changing at a rate of 9.65 x 10^-5 volts per meter per second. The direction of the electric field will be counter-clockwise, as you have correctly stated.

Overall, the key concept to understand is that a changing magnetic field induces an electric field in a conductor. This concept is crucial in many areas of physics and engineering, such as generators, transformers, and electromagnets.