Two charges Q1 =20uc and Q2=30uc are placed 30cm apart find the point of of zero potential on the side straight line between Q1 and Q2

Answer 1

The point of zero potential on the line between Q1 and Q2 can be found by using the formula for the electric potential due to point charges:

V = k * (Q1 / r1) + k * (Q2 / r2)

Where:
V = electric potential
k = Coulomb's constant (8.9875 x 10^9 N m^2/C^2)
Q1 = charge of Q1 (20 µC = 20 x 10^-6 C)
Q2 = charge of Q2 (30 µC = 30 x 10^-6 C)
r1 = distance of the point from Q1
r2 = distance of the point from Q2

Since the point is on the straight line between Q1 and Q2, r1 + r2 = 30 cm = 0.3 m

Let the distance from Q1 to the point be x, then the distance from Q2 to the point will be 0.3 - x

Substitute these into the formula and set V = 0 to find the point of zero potential:

0 = k * (Q1 / x) + k * (Q2 / (0.3 - x))

Solving for x:
0 = (8.9875 x 10^9 * 20 x 10^-6) / x + (8.9875 x 10^9 * 30 x 10^-6) / (0.3 - x)

0 = 179750 / x + 269625 / (0.3 - x)

Multiplying throughout by x(0.3 - x) to clear the denominators:

0 = 179750(0.3 - x) + 269625x

0 = 53925 - 179750x + 269625x

0 = 89725x - 53925
53925 = 89725x
x ≈ 0.6015 m

Therefore, the point of zero potential on the line between Q1 and Q2 is approximately 0.6015 m from Q1 and 0.3 - 0.6015 = 0.6985 m from Q2.