READ PLEASE: I KNOW ANSWER IS C, I WOULD LIKE TO KNOW THE PROCEDURE. 2. Conducti

Question

READ PLEASE: I KNOW ANSWER IS C, I WOULD LIKE TO KNOW THE PROCEDURE.

2. Conducting Sphere 1 with radius Ri has positive charge Q. Sphere 2 with radius R2 = 4R1 is far from sphere 1 and initially uncharged. After the separated spheres are connected with a wire thin enough to retain only negligible charge, (i) Which sphere has greater final charge? (ii) Which sphere has greater final surface charge density? (ii) Is the change in potential energy of the system +, -, or 0? A) (i) 2, (ii) Same, (iii) 0 B) (i) Same, i1, (iii) D) ) Same, (ii) Same, (ii) + E)i) 0

Explanation / Answer

charge on sphere1 , q1 = Q

charge on sphere2 , q2 = 0

after connecting with thin wire

charge flows until potential remains same

potential of sphere 1 = potential of sphere 2

V1 = V2

K*Q1/R1 = k*Q2/R2

Q1/R1 = Q2/R2

(Q - q)/R1 = q/(4R1)

Q - q = q/4

q = (4/5)*Q

charge on sphere1 , Q1 = Q - q = Q/5

charge on sphere 2 , Q2 = q = (4/5)*Q

(i) sphere 2 has greater final charge

(ii)

surface charge density of sphere1 = Q1/(4*pi*R1^2) = Q/(20*pi*R1^2)

surface charge density of sphere2 = Q2/(4*pi*R2^2) = Q/(*pi*R1^2) = Q/(80*pi*R1^2)

surface charge density of sphere1 has greater surface charge density

sphere 1

===================================

(iii)

initial potential energy = k*Q^2/R1

final potential energy Uf = k*Q1^2/R1 + k*Q2^2/R2 = kQ^2/5

change = Uf - Ui = -(4/5)*k*Q^2/R1

negative ' - '

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