Question

Two point charges lie on the x axis. A charge of 9.5 μC is at the origin, and a charge of -4.8 μC is at x = 10 cm.At what position x would a third charge q3 be in equilibrium? Express your answer using two significant figures.Give answer in cm

Answer 1

opposite charges attract while same charges repel.

so the new charge q3 can’t be in between the first two charges.

electric force between two charge Q1 and Q2 separated by a distance D is given by k*Q!*Q2/D^2

where k=coloumb’s constant

so for equlibrium, q3 should be closer to charge of lower magnitude.

hence it should be to the right of -4.8 uC.

let distance from -4.8 uC is d meters.

equating total forces to 0:

(k*9.5/(0.1+d)^2)-(k*4.8/d^2)=0

==>9.5*d^2=4.8*(d+0.1)^2

==>9.5*d^2=4.8*d^2+4.8*0.01+2*4.8*0.1*d

==>4.7*d^2-0.96*d-0.048=0

solving for d , we get d=0.2458 m=24.58 cm

so third charge q3 should be at x=10+24.58 cm=34.58 cm

in 2 significant figures,

answer=35 cm