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  4. Two infinite linear charges are placed parallel to each other at a distance 0.1 m from each other. If the linear charge density on each is 5 μ C / m, then the force (in N / m ) acting on a unit length of each linear charge will be

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Q. Two infinite linear charges are placed parallel to each other at a distance $0.1 \,m$ from each other. If the linear charge density on each is $5\, \mu C / m$, then the force (in $N / m$ ) acting on a unit length of each linear charge will be

Electric Charges and Fields

Solution:

Electric field at $2$ due to $1$,
image
$E=\frac{5 \times 10^{-6}}{2 \pi \varepsilon_{0}(0.1)}$
Force per unit length on wire$2$ ,
$F=E \times$ Charge on unit length of wire $2=E \times 5 \times 10^{-6}$
$=\frac{5 \times 10^{-6} \times 5 \times 10^{-6}}{2 \pi \varepsilon_{0} \times(0.1)}=4.5 \,N / m$