Two long parallel wires carry currents of equal magnitude but in opposite directions. These wires are suspended from rod PQ by four chords of same length L as shown in the figure. The mass per unit length of the wires is λ . Determine the value of θ assuming it to be small.
Text Solution
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Sol. The force per unit length between current carrying parallel wires is
= 
If two wires carry current in opposite directions the magnetic force is repulsive, due to which the parallel wires in Fig. have moved out so that equilibrium is reached. Fig shows free body diagram of each wire. In equilibrium,
Σ F y = 0, 2T cos θ = ( λ L 0 )g ….. (1)
Σ F z = 0, 2T sin θ = F B ….. (2)
Now dividing eqn. (2) by (1) we get
tan θ = 
….. (3)
The magnetic force F B = 
× L 0 = 
L 0 ….. (4)
For small θ , tan θ 
sin θ = θ
On substituting eqn. (4) in (3), we get
θ = I 
.
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