- Home
- Standard 12
- Physics
1. Electric Charges and Fields
medium
Two infinitely long parallel wires having linear charge densities ${\lambda _1}$ and ${\lambda _2}$ respectively are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$
A
$K\frac{{2{\lambda _1}{\lambda _2}}}{{{R^2}}}$
B
$K\frac{{2{\lambda _1}{\lambda _2}}}{R}$
C
$K\frac{{{\lambda _1}{\lambda _2}}}{{{R^2}}}$
D
$K\frac{{{\lambda _1}{\lambda _2}}}{R}$
Solution
(b) Force on $l$ length of the wire $2$ is
${F_2} = Q{E_1} = ({\lambda _2}l)\frac{{2k{\lambda _1}}}{R}$
$==>$ $\frac{{{F_2}}}{l} = \frac{{2k{\lambda _1}{\lambda _2}}}{R}$
Also $\frac{{{F_1}}}{l} = \frac{{{F_2}}}{l} = \frac{F}{l} = \frac{{2k{\lambda _1}{\lambda _2}}}{R}$
Standard 12
Physics
