Three point particles are arranged along the axes of a Cartesian coordinate syst
ID: 1704709 • Letter: T
Question
Three point particles are arranged along the axes of a Cartesian coordinate system. Each charge is a distance 0.5 m from the origin. The top particle lies along the positive y-axis and has a charge of +3 C while the other two particles lie along the positive and negative x-axis and each have a charge -4 C.
A. What is the electric field (magnitude and direction) at the origin?
B. What is the electric potential at the origin?
C. How much work was required to assemble this system of charges, assuming that each charge was originally very far away from the origin of this co-ordinate system and from each other?
Explanation / Answer
A. Electric field (intensity and direction) at any point according to the principle of superposition is the vector sum of field strengths, which are created by individual charges: E = E1 + E2 + ... + En
B. Similarly, the potential at the origin is equal to the algebraic sum of potentials of the fields that are created by each of the charges: = 1 + 2 + ... + n.
C. Work, according to the law of conservation of energy will be equal to the potential energy of a system of charges, the parameters are given in the problem.
Thus, the potential energy of interaction have charges
q1=+3 C q2=-4C; q1=+3 C q3=-4 C; q2=-4 C q3=-4 C.
W12 = kq1q2/r12 = 9·109·3·4/0.5 153·109J
W13 = kq1q3/r13 = 9·109·3·4/0.5 153·109J
Thus, the work is:
W23 = kq2q3/r23 = 9·109·3·4/0.5 = 108·109JW12+ W13+ W23 414·109 J 400·103M J.
Answer. 400·103M J.
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