Answer to Question #257131 in Electricity and Magnetism for zuzu

Question

a) Points A and B are at 0.05m and 0.03m from a charge +13 x10^-6C respectively. Determine the required work against the direction of the electric field to displace a charge +15 x10^-6C from point A to point B.

b) A charge q₁=+8 x10^-6C is at the origin (x=0mm), and other charge q₂=-3 x10^-6C is at x=60mm. Find the work done by the electric field if a charge q₃=-4 x10^-6C is displaced from point x=15mm to point x=5mm.

Answer 1

a)

$$W=(9\cdot10^{9})\frac{(15\cdot10^{-6})(13\cdot10^{-6})}{0.03}-\\(9\cdot10^{9})\frac{(15\cdot10^{-6})(13\cdot10^{-6})}{0.05}=23.4\ J$$

b)

$$E_1=(9\cdot10^{9})\frac{(3\cdot10^{-6})(4\cdot10^{-6})}{0.045}-\\(9\cdot10^{9})\frac{(8\cdot10^{-6})(4\cdot10^{-6})}{0.015}=-16.8\ J$$

$$E_2=(9\cdot10^{9})\frac{(3\cdot10^{-6})(4\cdot10^{-6})}{0.055}-\\(9\cdot10^{9})\frac{(8\cdot10^{-6})(4\cdot10^{-6})}{0.005}=-55.6\ J\\W=-55.6+16.8=-38.8\ J$$