Four equal point charges Q =10 nC are place at the four corners of a square 2 m on a side. Find the electric potential at the centre of the square.*1 point25.53 V20.50 V35.23 V28.42 V
Question
Four equal point charges Q =10 nC are place at the four corners of a square 2 m on a side. Find the electric potential at the centre of the square.*1 point25.53 V20.50 V35.23 V28.42 V
Solution
The electric potential V at a point due to a point charge Q is given by the formula:
V = kQ/r
where:
- k is Coulomb's constant (9 x 10^9 N.m^2/C^2),
- Q is the charge (in this case, 10 nC or 10 x 10^-9 C), and
- r is the distance from the charge to the point.
In this case, the distance from each corner to the center of the square is the diagonal of half the square, which can be calculated using Pythagoras' theorem:
r = sqrt((1 m)^2 + (1 m)^2) = sqrt(2) m
So the potential at the center due to one charge is:
V1 = kQ/r = (9 x 10^9 N.m^2/C^2) * (10 x 10^-9 C) / sqrt(2) m = 6.36 x 10^9 V
Since there are four charges, the total potential at the center is:
V_total = 4 * V1 = 4 * 6.36 x 10^9 V = 25.44 x 10^9 V
So the answer is approximately 25.44 V, which is closest to 25.53 V.
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