Question

Three charges are placed on the z-axis. There is a charge of +7.90 pC placed at z =-2.30 m, an unknown charge, Q, placed at x = +2.10 m; and a charge of +16.00 μC placed at x = +4.60 m. if the electric field at the point x = +1.00 m is to be exactly zero, what must be the sign and magnitude of the unknown charge, Q Number Units

Answer 1

Electric field at x = 1 m is known to be zero.

so, $E = k\left(\frac{7.9\mu}{(1-(-2.3))^2}+\frac{Q}{(2.1-1)^2}-\frac{16\mu}{(4.6-1)^2} \right )=0$

=> $\frac{7.9\mu}{10.89}+\frac{Q}{1.21}=\frac{16\mu}{12.96}$

therefore, Q = +6.16 x 10^-7 C

the magnitude of this charge is Q = 6.16 x 10^-7 C and it is positive in nature.