Question

can you solve this Q with details ?

The figure below shows four positive point charges q1= q2= q3= q4= +2 muC. A fifth (negative) charge q5= -1 muC is located at the origin. Calculate the net electric force acting on the fifth charge. Charge q4 can be moved along the Y-axis. To what y-value must charge q4 be moved to rotate the direction of the net electric force on charge q5 by 45 degree counterclockwise? Calculate the net electric force acting on the fifth charge under this new arrangement of charges.

Answer 1

Answer 2

Answer 3

3A)
net electric force acting on fifth charge,
FOrce on q5 because of q1 = ( K * q1 * q5) / r15^2 = (9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(0.02^2) i = -45 i
FOrce on q5 because of q2 = ( K * q2 * q5) / r25^2 = (9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(0.02^2) j = -45 j
FOrce on q5 because of q3 = ( K * q3 * q5) / r35^2 = -(9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(0.01^2) i = 180 i
FOrce on q5 because of q4 = ( K * q4 * q5) / r45^2 = -(9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(0.02^2) j = 45 j
So total force = (-45+180) i + (45-45) j = 135 i N
net electric force = 135 N in positive x direction
3B)
i)
If charge q4 is moved, the vertical component of net force changes
the force in y direction has to be equal to that of force in x direction, it has to be equal to 135 N in positive y direction.
so
if p is the y value of q4
FOrce on q5 because of q4 = ( K * q4 * q5) / r45^2 = -(9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(y^2) j
FOrce on q5 because of q2 = ( K * q2 * q5) / r25^2 = (9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(0.02^2) j = -45 j
so FOrce on q5 because of q4 = 135 + 45 = 180 N
so, -(9 *(10^9) * 2* (10^-6)*-1*(10^-6))/(y^2) = 180
y = 0.01 m = 1 cm
q4 has to be moved to y = 1 cm from y = 2 cm

ii)
net force =sqrt ( 135^2 + 135^2) = sqrt (2) * 135 = 190.918 N is the answer