Answer to Question #257131 in Electricity and Magnetism for zuzu

Question #257131

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.



1
Expert's answer
2021-10-26T17:17:53-0400

a)


W=(9109)(15106)(13106)0.03(9109)(15106)(13106)0.05=23.4 JW=(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)


E1=(9109)(3106)(4106)0.045(9109)(8106)(4106)0.015=16.8 JE_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

E2=(9109)(3106)(4106)0.055(9109)(8106)(4106)0.005=55.6 JW=55.6+16.8=38.8 JE_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



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