Question

The sum of two point charges is 7uc. They repel each other with a force of 1n Newton when kept 30 cm apart in free space. calculate the value of each charge.​

Answer 1

As,they repel each other,they must be like charges.

Let,they be

q1

and

q2

Given,

q1+q2=7*10^(-6)

Now, if 1N

force is acting in between them on keeping them

30cm apart ,then

1=9⋅10^9⋅q1⋅q2/(30/100) ^2

or,

q1q2=10^−11

Now,

(q1−q2)^2=(q1+q2)^2−4q1q2

so,

(q1−q2)=√(9⋅10^−12)=3⋅10^−6

So,solving the equations, we get,

q1=5⋅10^−6C

and

q2=2⋅10^−6C

(note,both can be negative together as well)

Answer 2

F = 1N

q1 + q2 = 7×10^-6C = 7uC

r = 30 × 10^-2 m = 30 cm

F = kq1q2/r^2 = q1q2/C

F = q1q2×10^9/900 × 10^-2 = 1

q1q2 = 10^-11

(q1-q2)^2 = (q1+q2)^2 - 4q1q2

= (7×10^-6)^2 - 4×10^-11

q1 - q2 = 3 × 10^-6

q1 = 5 × 10^-6 = 5uC

q2 = 2 × 10^-6 = 2uC