Question

Four objects, each carrying a charge of magnitude q

, are placed at the corners of a square measuring d
on each side. Two of the objects are positively charged, and two are negatively charged, with like-charged objects placed at opposite corners of the square.
Part A
Is the electric potential energy associated with this charge distribution positive, negative, or zero?
Is the electric potential energy associated with this charge distribution positive, negative, or zero?
positive
negative
zero
Request Answer
Part B
Confirm your answer to the previous part by calculating the electric potential energy.
Express your answer in terms of the variables q
, d
, and the Coulomb's law constant k
.

Answer 1

Step-by-step explanation:

Part A: The electric potential energy associated with this charge distribution is negative.

Explanation: The electric potential energy of a system of charges is given by the formula:

U = (1/4πε₀) Σ(i<j) qi*qj/r_ij

where U is the electric potential energy, qi and qj are the charges on objects i and j, r_ij is the distance between objects i and j, and ε₀ is the electric constant.

In this case, we have two positive charges and two negative charges, and they are arranged in a square configuration. The distance between any two charges is d√2, since they are at opposite corners of a square with sides of length d. Therefore, the electric potential energy of the system is:

U = (1/4πε₀) [2(q^2)/d√2 - 2(q^2)/d√2 - 2(q^2)/d√2 + 2(q^2)/d√2]

Simplifying this expression, we get:

U = (1/4πε₀) (0) = 0

Therefore, the electric potential energy associated with this charge distribution is zero.

Part B: As shown above, the electric potential energy associated with this charge distribution is zero.