Question

Two long, straight wires are parallel and 10 cm apart.One carries a current of 2.0 A, the other a current of 5.0A. (a) If the two currents flow in opposite directions, whatis the magnitude and direction of the force per unit lengthof one wire on the other? (b) What is the magnitude anddirection of the force per unit length if the currents flow inthe same direction?

Answer 1

Answer:

Explanation:

Given

Distance between two wires $d=10 cm$

Current value $i_1=2 A$

$i_2=5 A$

(a)If current flows in opposite direction

When current Flows in opposite direction the two wires will repel each other

Force due to current carrying wire $F=\frac{\mu _0i_1i_2}{2\pi r}$

$F_{12}=F_{21}=\frac{\mu _0\times 2\times 5}{2\times \pi \times 0.1}$

$F_{12}=\frac{4\pi \times 10^{-7}\times 2\times 5}{2\pi \times 0.1}$

$F_{12}=2\times 10^{-5} N$ (Repulsive Force)

(b)If current is flowing in the same direction

When direction of current is same then force will be attractive in nature

$F_{12}=F_{21}=\frac{\mu _0i_1i_2}{2\pi r}$

$F_{12}=\frac{4\pi \times 10^{-7}\times 2\times 5}{2\pi \times 0.1}$

$F_{12}=2\times 10^{-5} N$ (attractive Force)