Question

Please help. this is due in 30 minutes

Determine the resultant force acting on a point charge of -2 x 10^-6 C situated at the origin of a rectangular coordinate system in the vicinity of point charges 3 x 10^-6C and -4x 10^-6C at distances 0.12 m along the positive x-axis and 0.08m along the half-line y = x where x, y <= 0.

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Answer 1

Using Coulomb's Law, calculate the forces and sum their magnitudes to find the resultant force. After calculation the resultant force comes to be 6 N.

Step-by-step explanation:

To determine the resultant force acting on a point charge situated at the origin of a rectangular coordinate system in the vicinity of other point charges, we need to calculate the individual forces exerted by each charge and then vectorally add them. In this case, the point charge at the origin (-2 x 10^-6 C) is influenced by two other charges (3 x 10^-6C and -4x 10^-6C) located at distances 0.12 m and 0.08m, respectively.

Using Coulomb's Law, we can calculate the forces:

Force_1 = k * (q1 * q2) / r^2 = (9 x 10^9 N * m^2/C^2) * ((3 x 10^-6 C) * (-2 x 10^-6 C)) / (0.12m)^2

Force_2 = k * (q1 * q2) / r^2 = (9 x 10^9 N * m^2/C^2) * ((-4 x 10^-6 C) * (-2 x 10^-6 C)) / (0.08m)^2

Since both forces act along the x-axis, we can simply sum their magnitudes:

Resultant force = |Force_1| + |Force_2|

Calculating the values, we have:

Force_1 = 1.5 N

Force_2 = 4.5 N

Resultant force = 1.5 N + 4.5 N = 6 N