Identical point charges (+50 $\pm$C)are placed at the corners of a square with sides of 2.0-m length.How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square?
A)41 J
B)16 J
C)64 J
D)10 J
E)80 J

Question

Quizplus · Accepted Answer

The electric potential at the center of the square due to each charge can be found using the formula:

V = kq/r

Where V is the potential, k is Coulomb's constant, q is the charge, and r is the distance from the charge to the center of the square.

Since all charges are identical and equidistant from the center, the total potential due to all charges can be found by multiplying the potential due to one charge by the number of charges:

Vtotal = 4 * kq/r

The electric potential energy required to bring a fifth charge (+50 F) from infinity to the center of the square is given by:

U = qVtotal

U = (50 F) * (4 * k * 50 F / 2 m)

U = 800 kJ = 64 J

Therefore, the answer is C.

Identical Point Charges (+50 ±\pm± C)are Placed at the Corners of a Square with Sides

Identical Point Charges (+50 $\pm$ C)are Placed at the Corners of a Square with Sides