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Force between two parallel current carrying linear conductors

In this topic we will find the expression for Force between two parallel current carrying linear conductors when they are separated by some distance , and current flowing through them is in same direction ( also when current flowing through them is in different directions).

Before to know about In this topic  expression for Force between two parallel current carrying linear conductors when they are separated by some distance, students must know the expression for current carrying conductors placed in uniform magnetic field. To know about this topic click here

Force between two parallel current carrying linear conductors –

Two long straight conductors are placed parallel two each other at distance ‘r’  and current flowing through them are I1 and I2 . Since each conductors are carrying current produces magnetic field and hence each conductor experience force on each other.

As shown in figure (a) due to current I1 through C1D magnetic field at a point P on the wire C2D2 is B1 , then   B1 =  μ0I1 /2∏r ,

Since current flowing through the wire C2D2 is I2,

Then force experienced on the wire C2D2 is given as ,

F2 = B1 I2 l

Then  , Force per unit length F2/l = B1 I2 = μ0I1I2 /2∏r (Towards left i.e. towards C1 D1) .

Similarly , As shown in figure (b) due to current I2 through C2D magnetic field at a point Q on the wire C1D1 is B2 , then   B2 =  μ0I2 /2∏r ,

Since current flowing through the wire C1D1 is I1,

Then force experienced on the wire C1D1 is given as ,

F1 = B2 I1 l

Then  , Force per unit length F1/l = B2 I1 = μ0I1I2 /2∏r (Towards right i.e. towards C2 D2) .

So we can say if the current through each wire are in same direction then there will be force of attraction between them .

If the direction of current in the both the wires are opposite then there will be force of repulsion between them, as shown in figure ( c )below, with the same force  μ0I1I2 /2∏r .

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