Determine the direction of induced current in a wire

In summary, the conversation discusses the phenomenon of a wire experiencing a force when placed in a magnetic field, which is the basis for devices such as electric motors and galvanometers. The conversation also includes a diagram showing a uniform magnetic field and a coil being rotated through 360 degrees, with a question about determining the magnitude and direction of the current at each stage of the coil's motion. The solution involves using the equation for EMF and Fleming's right hand rule to determine the direction of electron flow.
  • #1
phosgene
146
1

Homework Statement



A wire carrying a current experiences a force when it is placed in a magnetic field. This phenomenon forms the basis of many devices including the electric motor and the gavlvanometer.

The diagram shows a uniform magnetic field B with magnitude 25mT directed towards the right. in the plane of the page. Initially, the coil ABCD is in the plane of the page. Each arm of the coil has length 1 = 50mm.

c) The current is turned off and the coil is rotated through 360 degrees about the axis shown. Sketch a graph showing the current flowing in the coil because of the induced emf as a function of the angular position of the coil. Explain how you determine the magnitude and direction of the current at each stage of the motion of the coil.

Homework Equations



EMF = 2NBlvsinx, where N = number of loops of wire, B = strength of magnetic field, l = length of wire, v = velocity of wire and x = angle subtending the magnetic field lines and coil of wire.

The Attempt at a Solution



If the velocity is constant, then the magnitude of the EMF is is determined by the angle x, and will be at a maximum when x = 90 degrees and at a minimum when x = -90 degrees.

I don't know how I can determine the direction of the current at each stage of the motion of the coil, however. The equation for EMF will tell me when it flows from positive to negative, but how can I tell which direction positive and negative are in?
 
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  • #2
It is a force on the electrons in the wire that causes the current to flow.
If you know your hand rule for that force F = q*v*B, you can use it to find the direction of electron flow.
 
  • #3
I think I got it now, I used Fleming's right hand rule. Thanks :)
 
  • #4
Most welcome. Interesting, I didn't know it was attributed to Fleming.
 
  • #5


To determine the direction of the induced current, you can use the right-hand rule. Place your right hand with your thumb pointing in the direction of the velocity of the wire and your fingers pointing in the direction of the magnetic field. The direction your palm is facing will indicate the direction of the induced current.

Alternatively, you can use Lenz's law, which states that the direction of the induced current will be such that it opposes the change in magnetic flux. This means that if the coil is rotated in a clockwise direction, the induced current will flow in the counterclockwise direction and vice versa.

In the given scenario, when the coil is in the plane of the page, the induced current will flow in the direction opposite to the current in the wire. As the coil is rotated, the direction of the induced current will change accordingly. The graph of induced current as a function of angular position will have a sinusoidal shape, with the sign of the current changing when the coil passes through the plane of the page.

In summary, the direction of the induced current can be determined using the right-hand rule or Lenz's law, and the graph of induced current as a function of angular position will follow a sinusoidal pattern.
 

What is induced current in a wire?

Induced current in a wire is the flow of electric charge that is generated in a conductor when it is exposed to a changing magnetic field. This phenomenon is known as electromagnetic induction and is the basis for the functioning of generators and transformers.

How is the direction of induced current determined in a wire?

The direction of induced current in a wire is determined by Lenz's Law, which states that the direction of the induced current will always oppose the change in the magnetic field that caused it. This means that if the magnetic field is increasing, the induced current will flow in the opposite direction to that of the changing field, and vice versa.

What factors affect the direction of induced current in a wire?

The direction of induced current in a wire is affected by the strength of the magnetic field, the speed at which the magnetic field changes, and the angle at which the wire is positioned in relation to the magnetic field. Additionally, the material and length of the wire can also impact the direction of the induced current.

What is the right-hand rule and how is it used to determine the direction of induced current?

The right-hand rule is a visual tool used to determine the direction of induced current in a wire. It states that if the thumb of your right hand points in the direction of the magnetic field, and your fingers point in the direction of motion of the wire, then the palm of your hand will point in the direction of the induced current.

What are some applications of induced current in a wire?

Induced current in a wire has many practical applications, such as in generators, transformers, electric motors, and electromagnetic sensors. It is also used in technologies like wireless charging and electromagnetic braking in trains and roller coasters.

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