Question

A uniform line of charge with length 20.0 cm is along the x-axis, with its midpoint at x= 0. Its charge per length is +5.80 nC/m. A small sphere with charge -2.00 μC is located at x = 0, y = 5.00 cm. What is the magnitude of the force that the charged sphere exerts on the line of charge?

Answer 1

The magnitude of the force that the charged sphere exerts on the line of charge is 2.48 * 10^-4 N.

Step-by-step explanation:

To find the magnitude of the force that the charged sphere exerts on the line of charge, we can use Coulomb's Law.

Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, the force between the charged sphere and the line of charge can be calculated using the following formula:

F = k * (q1 * q2) / r^2

Where F is the force, k is Coulomb's constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Substituting the given values:

F = (8.99 * 10^9 Nm^2/C^2) * ((-2.00 * 10^-6 C) * (5.80 * 10^-9 C/m * 0.20 m)) / (0.20 m)^2

F = -2.48 * 10^-4 N

Therefore, the magnitude of the force that the charged sphere exerts on the line of charge is 2.48 * 10^-4 N.