A positive and a negative charge are separated a distance r. What can we say about the electric potential energy of this two-particle system, according to our normal definitions of potential energy and work? Select the best answer.
a. It is positive
b. It is negative
c. It is zero
d. It is equal to the work done by the force
e. It is inverse to the work done by the force.
To determine the electric potential energy of a two-particle system, we need to consider the charges of the particles and their separation distance. The electric potential energy of a system is defined as the work required to assemble the system of charges from an infinite separation to their current positions.
The formula for electric potential energy is given by:
U = k * (|q1 * q2|) / r
Where:
U = electric potential energy
k = electrostatic constant (9 x 10^9 Nm^2/C^2)
q1, q2 = charges of the particles
r = separation distance between the charges
Now, let's consider the given scenario where we have a positive and a negative charge separated by a distance r. Since the charges have opposite signs (one positive and one negative), their product (|q1 * q2|) will always be negative.
Considering the formula for electric potential energy, we can see that the numerator will be negative, while the denominator (r) will be positive. Therefore, the overall electric potential energy, U, will be negative. This means that the correct answer is:
b. It is negative