Consider three long straight parallel wires as shown in figure. Find the force experienced by a 25 cm length of wire C.

Concept:

The magnetic field produced by a steady current flowing in a very long straight wire. The magnitude of the magnetic field is

\(B = \frac{{{\mu _0}I}}{{2\pi R}}\)

• Parallel wires carrying currents will exert forces on each other.
• Each wire produces a magnetic field, which influences the other wire. 
• When the currents in both wires flow in the same direction, then the force is attractive. 
• When the currents flow in opposite directions, then the force is repulsive.

The force exerted on wires can be given by:

\(F= \frac{{{\mu _0}}}{{2\pi }}\frac{{{I_1}{I_2}}}{{{r_1}}} \times Length\;of\;wire\)

Calculation:

Repulsion by wire D,       

\({F_1} = \frac{{{\mu _0}}}{{2\pi }}\frac{{{i_1}{i_2}l}}{r}\)   [towards right]

= \(\frac{{\left( {2 \;\times\; {{10}^{ - 7}}} \right)\left( {30\; \times\; 10} \right)}}{{3\; \times\; {{10}^{ - 2}}}}\left( {0.25} \right)\)

= 5 × 10^-4 N

Repulsion by wire G,

\({F_2} = \frac{{\left( {2\; \times\; {{10}^{ - 7}}} \right)\left( {20\; \times\; 10} \right)}}{{5\; \times \;{{10}^{ - 2}}}}\left( {0.25} \right)\)   [towards left]

= 2 × 10^-4 N

∴ F_net = F₁ – F₂

= 3 × 10^-4 N  [towards right]