PLEASE HELP AND SHOW WORK Question from Material in Chapter 17 A charge of -1.0

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PLEASE HELP AND SHOW WORK

Question from Material in Chapter 17 A charge of -1.0 C is located on the y-axis 1.0 m from the the coorrdinates (U.l origin at while a second charge of +1.0 C is located on the x-axis 1.0 in from the origin at the coordinates (1,0). Determine the value of the following quantities at the origin. The magnitude of the electric field, (6 points) The direction of the electric field, (1 points) lie electric potential (assuming the potential is zero at infinite distance). (S points) and l'he energy needed to bring a +1.0 C ellarge to this position from infinitely far away. 7 points

Explanation / Answer

The electric field along the y axis is

Ey = k q1 / R^2 = (8.99x10^9) (1) / (1)^2 = (8.99x10^9 N/C) j

The electric field along the x axis is

Ex = k q2 / R^2 = (8.99x10^9) (1) / (1)^2 = (8.99x10^9 N/C) i

The net field is

E = Sqrt [ Ex^2 + Ey^2 ] = Sqrt [ (8.99x10^9)2+ (8.99x10^9) ^2 ]  = 1.27x10^10 N/C

Direction is

theta = tan^-1 (Ey/Ex) = tan^-1 ((-8.99x10^9) /(8.99x10^9)) = 135

b)

The electric potential is

V =V1 + V2 = kq1 /R + k q2 /R = (8.99x10^9) (1) / (1) + (8.99x10^9) (1) / (1) = 1.798x10^10 volts

c) Work done in bringin a charge from infinity is

W = V x q = 1.798x10^10 ( 1 C) = 1.798x10^10 volts

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