Magnetic Effect Of Current

Using Amper’s circuital law to find magnetic flux density due to long current carrying conductor.

Let XY be a long straight wire carrying current i. Let ‘P’ is a point at a distance ‘a’ from the wire where magnetic field is to be found.
Let us consider a circle element dl at P.

Force per unit length is given by,

 ; 

where is the current in X.

i² is the current in Y.

R is the distance between them.    

Definition of Ampere: One ampere is the current which when flowing in each of the two infinitely long parallel conductors 1m apart in vacuum produces between them a force of  exactly 2 x 10^-7 N/m of length.

(i) Differences between moving coil galvanometer and tangent galvanometer, 

(ii) Cyclotron is particle accelerator. It is used to accelerate charged particles to high velocities by making them to pass repeatedly through the same accelerating region.

Force between two parallel current carrying conductors

Let parallel conductors are I and II. I₁, current is flowing through conductor I and I₂through II.

The force experienced per unit length by the current carrying conductor I due to the magnetic field produced by the conductor II. Magnetic field at point P due to current I₂ is given by,

According to right hand thumb rule, the direction of the magnetic field B₂ at point P is perpendicular to the plane of paper and in inward direction.

Now the conductor I carrying current I₁ lies in the magnetic filed B₂ produced by the conductor I₂.

Since, F = B I l

Hence, 
F = B₂ x (l₁ x I) = 
Force, F = 

Definition of Ampere:

Let I₁ = I₂ = 1 A and a = 1 m
Then from above equation, we have
One ampere is the current which when flowing through each of the two parallel conductors of infinite length and placed in free space at a distance of 1 metre apart, produces between them a force of 2 x 10 ^-7newton per metre of their lengths.