Question

A charge Q is located at x=0 and a charge 4Q is at x=12.0 cm. The force on a charge of −7μC is zero if that charge is placed at x=4.0 cm and is 674 N in the positive x direction if placed at x=8.0 cm. Determine the charge Q.

Answer 1

To determine the charge Q, use Coulomb's law and set up two equations using the given information. Solve the equations to find Q.

Step-by-step explanation:

To determine the charge Q, we can use the concept of electric force between charges. The force between two charges is given by Coulomb's law:

F = (k * Q1 * Q2) / r^2

Where F is the force, k is the electrostatic constant, Q1 and Q2 are the charges, and r is the distance between the charges.

Using the given information, we can set up two equations and solve for Q:

At x = 4.0 cm, the force is zero, so:

0 = (k * Q * (-7μC)) / (4.0 cm)^2

At x = 8.0 cm, the force is 674 N, so:

674 N = (k * Q * (-7μC)) / (8.0 cm)^2

Solving these equations will give us the value of Q.