Question

three point charges q1,q2,q3 are taken such that when q1 and q 2 are placed
close together to form a single point charge, the force on q3 at distance L from this
combination is a repulsion of 2 unit magnitude. When q2 and q3 are comnined
the force on q1 for same distance L is of magnitude 4 unit and is attractive.
Also a3 and q1 combining exerts a force of magnitude 18 unit in q2 from same
distance L. Algebraic ratio of charges q1,q2and q3, is
b. 2:-3:4
a. 1:2:3
d. 4:- 3:2
c 4:-3:1

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Answer 1

Answer:(b) is the correct answer.

Explanation:

2=(q1+q2).q3/L^2--------------(1)

-4=q1.(q2+q3)/L^2-------------(2)

18=(q1+q3).q2/L^2-------------(3)

Subtracting eq (1) and (2)----

2-(-4)=(q1q3+q2q3-q1q2-q1q3)/L^2

6=(q2q3-q1q2)/L^2

6=(q3-q1).q2/L^2

q2=6.L^2/(q3-q1)

Putting the value of q2 in eq (3)----

18=(q1+q3).q2/L^2

18.L^2=(q1+q3).q2

18.L^2/(q1+q3)=q2

18.L^2/(q1+q3)=6.L^2/(q3-q1)

By cross multiplication, we get----

3.q3-3.q1=q1+q3

2.q3=4.q1

q3=2.q1

q3/q1=2/1

Hence, q1:q3=1:2

By dividing eq (3) by (1), we get---

18/2=(q1q2+q2q3)/(q1q3+q2q3)

9=(q1q2+q2q3)/(q1q3+q2q3)

By cross multiplication, we get---

9.q1.q3+9.q2.q3=2.q1.q2+2.q2.q3

7.q2.q3=2.q1.q2-9.q1.q3

Putting the ratio of q1 and q3----

7.q2.2=2.1.q2-9.1.2

14.q2=2.q2-18

12.q2=-18

q2=-3/2

q1:q2:q3=1:-3/2:2

Multiplying the ratio by 2, we get---

q1:q2:q3=2:-3:4