please give solution of a multiplechoice question with 4 answers?

Question

QUESTION- Two charges q1 & q2 are placed 30cm apart ,as shown in the figure,(i have described below) A third charge q3 is moved along arc of circle of radius 40cm from point C to D .The change inpotential energy of system is kq3/ 4(pi)(ipsilin zero) then k=?
ANSWER:-
(a)8q2, (b)6q1, (c)8q1, (d)6q2

please say value of k=? & explain briefly

GIVEN PICTURE IS DESCRIBED AS GIVEN
Here A is centre of circle & a charge is placed (q1) , C & D are points on circle such that AC & AD are radius of circle (=40cm) & angle CAD = 90 .A charge q3 is placed at pointC & q2 is a charge at point B( a point on radius AD & its distance from point A is 30cm)

detail including mathematical

Answer 1

ANS;
a or b or c or d.
Probebility of each is 1\4

Answer 2

A orD .since change in potencial should include terms q2 and q3 cause orintation is changed but it only include q3 that means q1 was in k which cancelled.hope get better answer.

Answer 3

the distance of q(3) from q(1) remains same. final potential energy=kq(3){q(1) / 0.4 + q(2) / 0.1}

initial potential energy=kq(3){q(1) / 0.4 + q(2) / 0.5}

change in P.E.=final P.E - initial P.E

=kq(3){q(1) / 0.4 + q(2) / 0.1} - kq(3){q(1) / 0.4 + q(2) / 0.5}

=kq(3){q(2) / 0.1 - q(2) / 0.5}

=kq(3)q(2){10-2}

= kq(3)q(2) 8
here k is constant of electrostatics,its value is 1 /4 pi ipsilon not ipsilon aar(ipsilon aar is dielectric constant of the medium)
Hence (a) is the correct choice

Answer 4

the answer is C

Answer 5

this question is of Which standard

Answer 6

____1/4___