Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is .

Engineering

Physics

Electric Flux and Gauss Law and its Applications

Question

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is $a = \frac{\sqrt{3}}{2} L$ .

$\frac{Q}{3 {πε}_{0} L^{2}}$

$\frac{Q}{2 \sqrt{3} {πε}_{0} L^{2}}$

$\frac{Q}{4 {πε}_{0} L^{2}}$

$\frac{\sqrt{3} Q}{4 {πε}_{0} L^{2}}$

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$E = \frac{kλ}{a} ({sinθ}_{1} + {sinθ}_{2})$

$E = \frac{1}{4 {πε}_{0}} \times \frac{Q}{L} \times \frac{1}{(\frac{\sqrt{3} L}{2})} \times (2 sinθ)$

$tanθ = \frac{L / 2}{\frac{\sqrt{3} L}{2}} = \frac{1}{\sqrt{3}}$

$sinθ = \frac{1}{2}$

$E = \frac{1}{4 {πε}_{0}} \times \frac{2 Q}{\sqrt{3} L^{2}} \times (2 \times \frac{1}{2})$

$E = \frac{Q}{2 \sqrt{3} {πε}_{0} L^{2}}$