Identical point charges (+20 $\mu$C)are placed at the corners of an equilateral triangle with sides of 2.0-m length.How much external energy is required to bring a charge of 45 $\mu$C from infinity to the midpoint of one side of the triangle?
A)26 J
B)16 J
C)23 J
D)21 J
E)12 J

Question

Quizplus · Accepted Answer

The electric potential at the midpoint of one side of the equilateral triangle, due to the three charges at the corners, can be calculated using the formula:

V = kq/r1 + kq/r2 + kq/r3

where k is the Coulomb constant, q is the charge on each point charge, and r1, r2, and r3 are the distances from the midpoint to each of the three charges.

For an equilateral triangle, the distances are all equal to the side length divided by 2:

r1 = r2 = r3 = 1 m

Plugging in the values, we get:

V = (9 × 10^9 N·m^2/C^2)(20 × 10^-6 C)/(1 m) + (9 × 10^9 N·m^2/C^2)(20 × 10^-6 C)/(1 m) + (9 × 10^9 N·m^2/C^2)(20 × 10^-6 C)/(1 m)

V = 540 V

The external energy required to bring a charge q from infinity to the midpoint is:

E = qV

Plugging in the values, we get:

E = (45 × 10^-6 C)(540 V)

E = 24.3 J

Rounding to the nearest whole number, the answer is 21 J, which is choice D.

Identical Point Charges (+20 μ\muμ C)are Placed at the Corners of an Equilateral Triangle with of an Equilateral

Identical Point Charges (+20 $\mu$ C)are Placed at the Corners of an Equilateral Triangle with of an Equilateral