Three charges are at the corners of an equilateral triangle, as shown in the fig

Question

Three charges are at the corners of an equilateral triangle, as shown in the figure below. Calculate the electric field at a point midway between the two charges on the x-axis. (Let q1 = 5.50 ?C, q2 = 7.00 ?C, and q3 = ?4.50 ?C.) What is the magnitude and direction?

Three charges are at the corners of an equilateral triangle, as shown in the figure below. Calculate the electric field at a point midway between the two charges on the x-axis. (Let q1= 5.50pC q2-7.00,C, and q3=-4.50 C.) magnitude direction N/C o below the +x-axis 0.500 m 60.0°

Explanation / Answer

Electric field is given by

E = kQ/r^2

electic field due to q2

E1 = 8.99*10^9*7*10^(-6)/(0.25)^2 = 1006880 N/C

and direction is +x axis

electic field due to q3

E2 = 8.99*10^9*4.5*10^(-6)/(0.25)^2 = 647280 N/C

and direction is +x axis

now electric field by q2 and q3 = E1 + E2 = 1006880 + 647280 = 1654160 N/C

now distance from q1 = sqrt(0.5^2 - 0.25^2) = 0.433 m

so

electic field due to q1

E3 = 8.99*10^9*5.5*10^(-6)/(0.433)^2 = 263722.14 N/C

and direction is -y axis

so net electric field at point = sqrt(1654160^2 + 263722.14^2) = 1675050.6 N/C

theta = arctan(- 263722.14/1654160) = - 9.06 degrees

so direction is 9.06 degrees below the +x axis

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