Question

Two parallel wires carry currents in the same direction. If the currents in the wires are 1A and 4A and the wires are 5 m apart. Calculate the force between the 2 wires. Is it attractive or repulsive? Calculate the magnetic field midway between the wires.

Answer 1

Answer:

$1.6\times 10^{-7}$ N

$2.4\times 10^{-7}$ N

Explanation:

$i_{1}$ = 1 A

$i_{2}$ = 4 A

$r$ = distance between the two wire = 5 m

$F$ = Force per unit length acting between the two wires

Force per unit length acting between the two wires is given as

$F = \frac{\mu _{o}}{4\pi }\frac{2i_{1}i_{2}}{r}$

$F = (10^{-7})\frac{2(1)(4)}{5}$

$F = 1.6\times 10^{-7}$ N

$r'}$ = distance of each wire from the midpoint = 2.5 m

Magnetic field midway between the two wires is given as

$B = \frac{\mu _{o}}{4\pi } \left \left ( \frac{2i_{2}}{r'} \right - \frac{2i_{1}}{r'} \right \right ))$

$B = (10^{-7}) \left \left ( \frac{2(4)}{2.5} \right - \frac{2(1)}{2.5} \right \right ))$

$B = 2.4\times 10^{-7}$