Question

A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge -2.02 nC is placed on the positive x-axis at x= 3.98 cmcm . A third particle, of charge 5.95 nC is now placed at the point x = 3.98 cm , y = 3.04 cm .

Find the x-component of the total force exerted on the third charge by the other two.
Express your answer in newtons.

Answer 1

To find the x-component of the total force exerted on the third charge, calculate the individual forces and sum them up using Coulomb's Law.

Step-by-step explanation:

To find the x-component of the total force exerted on the third charge by the other two charges, we need to calculate the force exerted by each individual charge and then add them up. The force between two charges can be calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's denote the charge at the origin as Q1 = 4.98 nC, the charge on the positive x-axis as Q2 = -2.02 nC, and the charge at the point (3.98 cm, 3.04 cm) as Q3 = 5.95 nC.

The force between Q3 and Q1 is given by:

F13 = k * |Q3| * |Q1| / r13^2

Similarly, the force between Q3 and Q2 is given by:

F23 = k * |Q3| * |Q2| / r23^2

Finally, the x-component of the total force Fx is the sum of the x-components of F13 and F23:

Fx = F13 * cos(theta13) + F23 * cos(theta23)

Substituting the values and calculating, you can find the x-component of the total force.