Four Point Charges are fixed a thte corners of a 3.0 m by 4.0 m rectangle as sho

Question

Four Point Charges are fixed a thte corners of a 3.0 m by 4.0 m rectangle as shown. Compute the net electrostatic force (in Newtons) acting on the +55 microcoulomb charge. Give both the x and y components of the force and also the magnitude and direction of the force.

1. Four point charges are fixed at the corners of a 3.0 m by 4.0 m rectangle as shown. Compute the net electrostatic force in Newtons) acting on the +55 microcoulomb charge. Give both the x and y components of the force and also the magnitude and direction of the force. arts A 4.0 m 3,On 3, On arts

Explanation / Answer

The rectangle compnents

x = 4 m and y = 3 m

the length of the corner is

r = 5 m

the electric field at charge +55*10^-6 C is

E = k*q/r

= (9*10^9)*(55*10^-6)/5

= 99.0*10^3 N/C

the angle of 45 degree

the x_component is

E_x = (99.0*10^3)*cos(45)

= 70.00*10^3 N/C

the y_component is

E_y = (99.0*10^3)*sin(45)

= 70.00*10^3 N/C

The magnitude of electric filed at charge 55*10^-6 C is

E = sqrt[(70.00*10^3)^2 + (70.00*10^3)^2]

= 98994.949 N/C

And direction is

tan(theta) = E_y/E_x

= (70.00*10^3)/(70.00*10^3)

theta = 45 degree

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