Answer to Question #164207 in Electricity and Magnetism for willow

Question

A charge of -1.0 nC is located on the y-axis 1.0 m from the origin at the coordinates (0,1) while a second charge of +1.0 nC is located on the x-axis 1.0 m from the origin at the coordinates (1,0). Determine the value of the following quantities at the origin…a. the magnitude of the electric field b. the direction of the electric field c. the electric potential (assuming the potential is zero at infinite distance) d. the energy needed to bring a +1.0 nC charge to this position from infinitely far away 

Answer 1

Answer

(A)magnitude of electric field due to point charge at origin

$E_1=E_2=\frac{(9\times10^9) (1.0nC) }{1^2}=9N/C$

$E_{net}=\sqrt{E_1^2+E_2^2}=9\sqrt{2}N/C$

(b) magnitude of E1 and E2 are equal so direction of electric field will be make 45° angle with +ve X-AXIS.

(C) electric potential at origine

$V=\frac{9\times10^9(1nC)}{1}+\frac{9\times10^9(1nC)}{1}\\V=18volts$

d) work done will be equal to change in electric potential energy

$W=\Delta U= (9\times10^9) [ [ \frac{ (-1nC) (1nC) }{\sqrt{2}}+\frac{(1nC) (1nC) }{1}+\frac{(-1nC) (1nC)}{1}]-[\frac{(1nC) (-1nC) }{\sqrt{2}}]]$

$W=0J$