Four point chares are equally separated by 1.00m in air. If q1 = 3.0 nC, q2 = -4.0 nC, q3 = 2.0 nC, and q4 = -5.0 nC, what is the electric field at a point halfway between q2 and q3?
Answers
Answer:
each of the charges individually.
All four charges are equidistant from the center (a distance r in the figure). If two diagonal charges have the same magnitude and sign, then the electric field at the center due to these two charges have equal magnitude and opposite directions. Their resultant is, therefore, zero. Thus, the electric field at the center will be zero if each diagonal pair of charges has the same magnitude and sign.
If a diagonal pair of charges has the same magnitude and sign, they will give rise to a non-zero potential at the center. Thus, the potential due to one diagonal pair of charges must cancel the potential due to the other diagonal pair of charges. This will be the case if the two pairs of diagonal charges have opposite signs.
Thus, both the electric field and the electric potential will be zero at the center of the square if all four charges have the same magnitude, q1 and q3 have the same sign, and q2 and q4 have the same sign, which is opposite to the signs of q1 and q3.