## Sunday, September 4, 2016

### Torque acting on a rectangular coil

A rectangular coil can be placed between two strong poles of a magnet. If we pass current in that coil, around it in the perpendicular plane, a magnetic field is developed. Thus the coil is under the influence of two magnetic fields. Thus one pair of the sides of the coil experience a pair of forces acting in the opposite direction but at two different edges of the coil. That pair of forces generate a couple and turns the coil in a particular direction. Thus there is a torque developed in the coil and here we are interested in measuring it in the present lesson.

Let us consider a rectangular coil carrying current in it. Hence there is a magnetic field around it. Let us assume that it is placed between two poles of a magnet. We know that the current carrying conductor placed in a magnetic field experience a force. Thus each part of the rectangular coil experience a force. Any way this force in the horizontal sides of the coil is not going to produce any torque as it is acting along the length of the coil.

We can show the coil with current and the forces as shown below. If the coil is having number of turns, we shall count the force due to all turns by multiplying with the number of turns. The other two sides does not experience any force as the direction of the current and the magnetic field is same and hence the force due to magnetic field is zero.

The other two forces together constitute a couple and turns the coil. Thus a torque is developed and we can measure the torque as the product of any one force and the perpendicular distance between the two forces. We can measure it as shown in the diagram below.

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