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Question
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
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Solution
Let a and b be long straight parallel conductors. Ia and Ib are the current flowing through them and are separated by a distance d.
Magnetic field induction at a point P on a conductor b due to current Ia passing through a is
\[B_1 = \frac{\mu_0 2 I_a}{4\pi d}\]
Now, unit length of b will experience a force as
\[F_2 = B_1 I_b \times 1 = B_1 I_b \]
\[ \therefore F_2 = \frac{\mu_0}{4\pi}\frac{2 I_a I_b}{d}\]
Conductor a also experiences the same amount of force, directed towards b. Hence, a and b attract each other.
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