Question
Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current of $$'i'$$ $$A$$ in the same direction. They will
A.
repel each other with a force of $$\frac{{{\mu _0}{i^2}}}{{\left( {2\pi d} \right)}}$$
B.
attract each other with a force of $$\frac{{{\mu _0}{i^2}}}{{\left( {2\pi d} \right)}}$$
C.
repel each other with a force of $$\frac{{{\mu _0}{i^2}}}{{\left( {2\pi {d^2}} \right)}}$$
D.
attract each other with a force of $$\frac{{{\mu _0}{i^2}}}{{\left( {2\pi {d^2}} \right)}}$$
Answer :
attract each other with a force of $$\frac{{{\mu _0}{i^2}}}{{\left( {2\pi d} \right)}}$$
Solution :
$$\frac{F}{\ell } = \frac{{{\mu _0}{i_1}{i_2}}}{{2\pi d}} = \frac{{{\mu _0}{i^2}}}{{2\pi d}}$$
(attractive as current is in the same direction)
$$\frac{F}{\ell } = \frac{{{\mu _0}{i_1}{i_2}}}{{2\pi d}} = \frac{{{\mu _0}{i^2}}}{{2\pi d}}$$
(attractive as current is in the same direction)
