# How Does Rotating a Semicircular Wire Loop Affect Magnetic Flux?

• rcmango
In summary: B}.You need to find the area swept out in time t, and the angle that the normal to this area makes with the magnetic field. In summary, the question asks for the change in the magnetic flux through a loop of wire as it is rotated through half a revolution, with one part forming a semicircle of radius r = 0.24 m. The normal to the loop is parallel to a constant magnetic field with magnitude 0.75 T. The solution involves finding the area swept out in time t and the angle between the area normal and the magnetic field.
rcmango

## Homework Statement

A loop of a wire has the shape shown in the drawing. The top part of the wire is bent into a semicircle of radius r = 0.24 m.

The normal to the plane of the loop is parallel to a constant magnetic field ( = 0°) of magnitude 0.75 T. What is the change in the magnetic flux that passes through the loop when, starting with the position shown in the drawing, the semicircle is rotated through half a revolution?
Wb in weber

here is a pic: http://img213.imageshack.us/img213/4917/75104403bx0.png

## The Attempt at a Solution

not sure where the time comes from, how to figure that out from the diagram.

also, are A0 = x0*L

that is the area swept out in time t.

need help finding the variables for this one.

also, i know that I need to find the angle A and B make at time t.

I need help on how to do this.

Last edited by a moderator:
So what you probably want to do in your imagination is rotate the loop and figure out how the area vector's normal changes. After all, flux will only go through the parts of the loop that are parallel to the magnetic field. How do the components of the area normal vary in time if we call the angular velocity of rotation omega?

The math formalism you want is essentially

$$\Phi = AB\matbf{\hat{n}}(t)$$

Last edited:

Dear student,

The change in magnetic flux through a loop is given by the equation ΔΦ = BAcosθ, where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the normal to the loop and the magnetic field.

In this problem, the magnetic field strength and the area of the loop are given, so we just need to find the change in angle θ as the loop is rotated through half a revolution.

To do this, we can use the fact that the normal to the loop is always parallel to the magnetic field. At the starting position shown in the drawing, the normal is pointing directly to the right (θ = 0). As the loop is rotated through half a revolution, the normal will end up pointing directly to the left (θ = 180°).

Therefore, the change in angle θ is 180°, and the change in magnetic flux is given by ΔΦ = BAcos180° = -BA.

Since the area and magnetic field strength are given in the problem, you can calculate the change in magnetic flux in webers. I hope this helps!

## 1. What is meant by change in magnetic flux?

Change in magnetic flux refers to the change in the amount of magnetic field passing through a given area. It can be caused by a change in the strength or direction of the magnetic field, or by a change in the size or orientation of the area.

## 2. How is change in magnetic flux calculated?

Change in magnetic flux is calculated by taking the derivative of the magnetic flux with respect to time. This is represented by the formula ∆Φ/∆t, where ∆Φ is the change in magnetic flux and ∆t is the change in time.

## 3. What is the relationship between change in magnetic flux and Faraday's law?

Faraday's law states that a changing magnetic field will induce an electric current in a conductor. Therefore, a change in magnetic flux will result in the production of an electric current in a conductor, according to Faraday's law.

## 4. What factors can cause a change in magnetic flux?

A change in magnetic flux can be caused by a variety of factors, including a change in the magnetic field strength, a change in the orientation of the magnetic field, a change in the size or shape of the area, or a movement of the area in relation to the magnetic field.

## 5. How is change in magnetic flux used in practical applications?

Change in magnetic flux is used in various practical applications, such as electric generators, transformers, and motors. It is also important in understanding the behavior of electromagnetic waves and in technologies such as MRI machines and magnetic levitation systems.

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