An infinite conducting grounded plane is located at z = d/2. One charge q is loc
ID: 1283094 • Letter: A
Question
An infinite conducting grounded plane is located at z = d/2. One charge q is located at the point (O,O,d). A second charge ?q is located at the point (d,O,d). a. Where are the mirror charges located? b. What is the total induced charge on the grounded plane? c. What is the total force exerted on charge q in this system? d. What is the total energy needed to assemble the system of charges?
An infinite conducting grounded plane is located at z = d/2. One charge q is located at the point (0,0,d). A second charge -q is located at the point (d,0,d). a. Where are the mirror charges located? b. What is the total induced charge on the grounded plane? c. What is the total force exerted on charge q in this system? d. What is the total energy needed to assemble the system of charges?Explanation / Answer
1. The mirror charges are located at the back of the conducting plane at the same distance as the real charge is in fron of them. So the mirror charge for q(0,0,d) is located at (0,0,0) with a magnitude of -q. And the mirror charge for -q(d,0,d) is located at (d,0,0) with a magnitude of +q.
2. The charge induced on the plane by a point charge is equal to negative magnitude of the charge. So the charge induced by q is -q ans by -q is +q.
So total charge = -q + q = 0
3. Forc on charge q is the vector sum of the forces exerted by the real as well as mirror charges.
Fq = F-q(d,0,d) + F-q(0,0,0) + Fq(d,0,0)
= -kq2/d2cos450 + -kq2/d2cos450 + kq2/2d2
= -root(2)kq2/d2 + kq2/2d2
the component of cos comes when we resolve the force vectors of the charges 900 each other and k = 9x109
4. The energy required to assemble the c=system is equal to bringing the real charges to their positions i.e.
energy = kq*-q/d = -kq2/d