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 q at distance r from it is φ=krq, where k=4πϵ01=9⋅109N⋅m2⋅C−2 is Coulomb's constant.
Point A is at distance rA=32+32=32 from charge at (0,0), and point B is at distance rB=2.
Hence, φA=32m9⋅109Nm2C−2⋅3⋅10−9C≈6.4V and φB=2m9⋅109Nm2C−2⋅3⋅10−9C≈13.5V.
Work needed to take charge q=2⋅10−9C from point A to point B is A=q(φA−φB)≈−1.42⋅10−8J.
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