Answer to Question #118747 in Electricity and Magnetism for shaine custodio

Question #118747
A particle of charge 3 x 〖10〗^(-9) C is located at point (0, 0) in a certain coordinate system. Assuming all lengths are in meters, calculate the potential at the following points A (3, 3) and B (0, 2). How much work is needed to take a particle of charge 2 x 〖10〗^(-9) C from point A to point B?
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Expert's answer
2020-05-29T09:48:02-0400

Potential created by a point charge qq at distance rr from it is φ=kqr\varphi = k \frac{q}{r}, where k=14πϵ0=9109Nm2C2k = \frac{1}{4 \pi \epsilon_0} = 9 \cdot 10^9 N \cdot m^2 \cdot C^{-2} is Coulomb's constant.

Point A is at distance rA=32+32=32r_A = \sqrt{3^2 + 3^2} = 3 \sqrt{2} from charge at (0,0)(0,0), and point B is at distance rB=2r_B = 2.

Hence, φA=9109Nm2C23109C32m6.4V\varphi_A = \frac{9 \cdot 10^9 N m^2 C^{-2} \cdot 3 \cdot 10^{-9} C}{3 \sqrt{2} m} \approx 6.4 V and φB=9109Nm2C23109C2m13.5V\varphi_B = \frac{9 \cdot 10^9 N m^2 C^{-2} \cdot 3 \cdot 10^{-9} C}{2 m} \approx 13.5 V.

Work needed to take charge q=2109Cq = 2 \cdot 10^{-9} C from point A to point B is A=q(φAφB)1.42108JA = q (\varphi_A - \varphi_B) \approx -1.42 \cdot 10^{-8} J.


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