## Thursday, September 1, 2016

### Force on Current Carrying Conductor Fleming Left Hand Rule

We can find the magnetic field around a wire on the axial line of charge using the Biot-Servert’s law. We are not adding the derivation here and the expression is as shown in the figure.

Let us consider a point on the axial line at a particular distance and let us assume that we know the radius at any given point.

The expression for the magnetic field at any point can be expressed as shown in the diagram. If we are measuring it at the center of the circle, we need to equate the value to zero.

We can also find out the force acting basing on Biot-Servert’s law. We can find the magnetic field at any given point using this rule. We know that the magnetic induction is defined as the force experienced by a unit north pole when placed in a magnetic field.

Thus we can measure the force as the product of the pole strength and magnetic induction. As the field is small component, the force is also small component. To get the total force acting on the point, we need to integrate the given equation and we can get the total force as shown in the diagram below.

This force will be maximum when the point is perpendicular to the current carrying conductor. If  the angle is zero or 180 degree, the force will become zero as shown below.

To  find  the  direction of the force experienced  by  the current carrying conductor using Fleming Left hand rule. As per the law, if  fore finger  indicate the direction of the magnetic  field and central finger indicates  the direction  of the  current then the thumb  indicates the direction of the thrust or force experienced by the current carrying conductor.

We  can also measure the force acting on  a charge simply by defining  the current as the rate of charge. We can define as the cross product of velocity of the charge and the magnetic field and the product is multiplied  with the charge.

We can  define  the  unit of  magnetic  induction tesla basing  on the above derivation. The magnetic  field induction is the force experienced by the  conductor when a  unit charge passing through  a conductor with unit velocity  at right angle.

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