find the charge

Question

An electric field is measured to be 7.16 x 10^2 N/C at a distance of 117.0 nm near an unknown charge. What is the value of the unknown charge?

Answer 1

We have the following:

electric field = electric force constant * unknown charge / distance^2 (or E = k*Q / r^2),

so electric field * distance^2 = electric force constant * unknown charge (or E*r^2 = k*Q),

so unknown charge = electric field * distance^2 / electric force constant (or Q = E*r^2 / k),

so by plugging in E = electric field = 7.16 * 10^2 N/C and r = 117.0 nm = 1.170 * 10^(-7) m,

we get that the unknown charge is:

Q = (7.16 *10^2 N/C) * (1.170 * 10^(-7) m) / (8.99 * 10^9 N*m^2/C^2) = 9.318 * 10^(-15) C.