A positive charge +q1 is located to the left of a negative charge −q2 On a line passing through the two charges, there are two places where the total potential is zero. The reference is assumed to be at infinity The first place is between the charges and is 4.80 cm to the left of the negative charge. The second place is 7.35 cm to the right of the negative charge if q2=−12μC , what is the value of charge q1∈μC?

Explanation:

At the point where net potential is zero , magnitude of potential will be equal .

At point between the given charges potential can be expressed as follows

k q₁ / d x 10⁻² = k 12 x 10⁻⁶ / 4.8 x 10⁻² ( q₁  charge is at distance d from the point )

At other point  potential due to both the charges  can be expressed as follows

k q₁ / (d+12.15) x 10⁻²  = k 12 x 10⁻⁶ / 7.35 x 10⁻²

(d+12.15) / d = 7.35 / 4.8

4.8 d + 58.32 = 7.35 d

2.55 d = 58.32

d = 22.87

Putting this value in first equation

k q₁ / d x 10⁻² = k 12 x 10⁻⁶ / 4.8 x 10⁻²

q₁ / 22.87 =  12 x 10⁻⁶ / 4.8

q₁ = 57.17 x 10⁻⁶

=  57.17 μC