In the following figure of a square with each side a=10 cm and three electric ch

Question

In the following figure of a square with each side a=10 cm and three electric charges q1=+15 microC, q2=-12 microC, and q3=+10 microC take the corners as shown. A test charge qtest=+1 microC is located in the remaining corner.

a) Find the net electric forces Fnet exert on qtest by q1, q2, and q3

b)Find the electric field Enet at the position of qtest

c) Find the electric potential energy U of qtest and the electric potential V at location of qtest

Explanation / Answer

Part A)

Apply F = kqq/r^2

From q1

F = (9 X 10^9)(15 X 10^-6)(1 X 10^-6)/(.1)^2 = 13.5 N downward

From q2

F = (9 X 10^9)(12 X 10^-6)(1 X 10^-6)/(.1414)^2 = 5.4 N

This one will have x and y components

x and y are 5.4(cos 45) = 3.82 N upward and to the right

From q3

F = (9 X 10^9)(10 X 10^-6)(1 X 10^-6)/(.1)^2 = 9 N to the left

The net x = 9 -3.82 = 5.18 N to the left

The net y = 13.5 - 3.82 = 9.68 N down

The net force is from the pythagorean theorem

net^2 = (5.18^2) + (9.68)^2

Net = 11.0 N

Part B)

For the electric field

F = qE

11 = (1 X 10^-6)(E)
E = 1.10 X 10^7 N/C

Part C)
PE = kqq/r

PE = (9 X 10^9)(1 X 10^-6)(15 X 10^-6)/.1 + (9 X 10^9)(1 X 10^-6)(-12 X 10^-6)/.1414 + (9 X 10^9)(1 X 10^-6)(10 X 10^-6)/.1

PE = 1.49 J

PE = qV

1.49 = (1 X 10^-6)(V)

V = 1.49 X 10^6 V

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