Question

There are four charges, each with a magnitude of 2.06 µC. Two are positive and two are negative. The charges are fixed to the corners of a 0.41-m square, one to a corner, in such a way that the net force on any charge is directed toward the center of the square. Find the magnitude of the net electrostatic force experienced by any charge.

Answer 1

0.208 N

Step-by-step explanation:

We are given that

`q_1=q_2=2.06\mu C=2.06* 10^(-6) C`

`q_3=q_4=-2.06\mu C=-2.06* 10^(-6) C`

Distance,d=0.41 m

The magnitude of the net electrostatic force experienced by any charge at point 4

Net force,
`F_(net)=\sqrt{F^2_1+F^2_3+2F_1F_3cos90^(\circ)}-F_2`

`F_1=F_3=F`

`F_(net)=√(F^2+F^2+0)-F_2`

`F_(net)=\sqrt 2F-F_2`

`F=(kq^2)/(d^2)`

`F_2=(Kq^2)/(2d^2)`

`F_(net)=(\sqrt 2kq^2)/(d^2)-(kq^2)/(2d^2)=(kq^2)/(d^2)(\sqrt 2-(1)/(2))`

Where
`k=9* 10^9`

`F_(net)=(9* 10^9* (2.06* 10^(-6))^2)/((0.41)^2)(\sqrt 2-(1)/(2))`

`F_(net)=0.208 N`