The figure shows three point charges. Charge 1 and Charge 2 are on the x-axis, a

Question

The figure shows three point charges. Charge 1 and Charge 2 are on the x-axis, and Charge 3 is one the y axis. The value of the charges are Charge 1 equal to Q, charge 2 equal to 2Q, and Charge 3 equal to q. All the charges are equal distance, d, from the origin (x = y = 0).

If Q = 4.0 nC, q = -0.6 nC, and d = 0.14 m, what is the magnitude of the total electric field at the origin, (x = y = 0)?

Give your answer to three significant digits in units of N/C. Do not include the units in your answer.

Explanation / Answer

Here ,

as the electric field due to a charge is given as

E = k * Q/d^2

Now , for the electric field at origin

in x-direction

Ex = k * (2Q - Q)/d^2

Ex = 9*10^9 * 4 *10^-9/.14^2

Ex = 1836.7 N/C

Now , in y direction

Ey = k *q/d^2

Ey = 9*10^9 * 0.6 *10^-9/.14^2

Ey = 275 N/C

Now , for the magnitude of electric field

E = sqer(Ex^2 + Ey^2)

E = sqrt(275^2 + 1836.7^2)

E = 1857 N/C

the magnitude of total electric field at the origin is 1857 N/C

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