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Force on a Current – Carrying Conductor in a Magnetic Field

Oersted's experiment clearly established that a current carrying wire exerts a force on a magnet such as a compass needle. By Newton's third law, the reverse should also be true. The magnet should also exert an equal and opposite force on the wire carrying the current. In the year 1821, Michael Faraday discovered that when a wire carrying a current is placed in the field of a magnet, a mechanical force is exerted on the wire.

 
When a current carrying conductor is placed in a magnetic field, it experiences a force, except when it is placed parallel to the magnetic field.
 
 
The given Figure illustrates an experiment to demonstrate the force exerted by a magnet on a current carrying wire and to show how the direction of the force is related to the direction of the current and the direction of the magnetic field.
 

 
A conducting rod of aluminum or copper is suspended horizontally between the poles of a horse-shoe magnet by means of two insulated wires as shown in Figure. The direction of the field is upwards, i.e. from the north pole towards the south pole. When key K is closed, a current flows in the rod from B to A. The rod is immediately kicked to the right. If the direction of the current is reversed, the rod is kicked in the opposite direction. The direction of the force exerted on the rod is perpendicular to the direction of the current and the direction of the magnetic field. The direction of the force is reversed also when the direction of the field is reversed. This is done by turning the magnet over so that its N pole is at the position previously occupied by its S pole.

Fleming's Left-Hand Rule

We have observed in the above experiment that the current, the magnetic field and the force are mutually at right angles to each other. J.A. Fleming gave a rule which may always be relied upon when we wish to determine the direction of the force exerted on a current carrying wire in a magnetic field. The rule is called Fleming's left hand rule. 
 
 
Hold the thumb and the first two fingers of your left hand mutually at right angles to each other as shown in Figure. Then if the Forefinger points in the direction of the Field, and the second finger in the direction of the Current, the thumb will point in the direction of Mot of the conductor.

 

Note
 
It is misleading to say that the magnetic field exerts a force on the wire. In fact a magnetic field exerts a force on any moving charge, whether the charge is moving in free space or in a metallic wire. A moving charge constitutes an electric current. Since the charges moving in a wire are confined to the body of the wire, the wire itself experiences a force.

 

Cause for force acting on a current carrying conductor
  • The force acting on a current carrying conductor in a magnetic field is due to interaction between Magnetic field due to current carrying conductor and External magnetic field in which the conductor is placed. The resultant of these two magnetic fields is not uniform. It is weaker on one side of the conductor then on its other side. The conductor, therefore, experiences a resultant force in the direction of the weaker magnetic field.
Do you know? A copper wire placed between the poles of bar magnets carries a current as shown in the diagram below. In which direction is the force acting on the wire?
 
  • upwards.
  • towards the magnet on the right.
  • towards the magnet on the left.
  • in the direction of the current flow.
  • in the direction opposite to the current flow.
  • downwards
A stream of positively charged particles (alpha particles) moving towards west is deflected towards north by a magnetic field. The direction of magnetic field is:
  1. towards south
  2. towards east
  3. downward
  4. upward
Think you are sitting in a chamber with your back to one wall.
 
An electron beam moving horizontally from back wall towards the front wall is deflected by a strong magnetic field to your right side.
 
Example

What is the direction of magnetic field?

Solution

Here the electron beam is moving from our back wall to the front wall, so the direction of current will be in the opposite direction, from front wall towards back wall or towards us. The direction of deflection (or force) is towards our right side.

 
We now know two things;
  1. Direction of current is from front towards us and
  2. Direction of force is towards our right side. Let us now hold the forefinger, centre finger and thumb of our left hand at right angles to one another. We now adjust the hand in such a way that our center finger points towards us (in direction of current) and thumb points towards right side (in the direction of force).
Now, if we look at our forefinger, it will be pointing vertically downwards is the direction of magnetic field. The mechanical effect of current was the foundation for the construction of the electric motor. 

 





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