A positive point charge q1 at the origin and a negative charge q2 at x=2m. The resultant electric field is 10.8 i N/C at x=1m and -8 i N/C at x=3m. Find q1 and q2.
We need to establish the two equations to determine the total electric field at x=1m and x=3m. The electric field is equal to . We know that q1>0 and q2<0, k=9X109 Nm2/C2, and for the first case at x=1 m, r1=r2=1m while . On the second case at x=3m we have r'1=3m, r'2=1m, and . Using that information we find the total electric field as ET=E1+E2:
The system that has to be solved is:
After solving, in conclusion, q1 = 2.8 X 10-10 C and q2= -9.2 X 10-10 C.
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