A +4 µC point charge is in the x-y plane at the point (3.0 m, 0.0m)

while a +10 µC point charge is at the point (0.0 m, 1.0 m).
(a) Express the Coulomb force on the +10 µC point charge due to the +4 µC charge in vector notation.
(b) What is the magnitude of the force. Note: The Coulomb is a very large unit of charge and so microcoulombs or µC are often used in calculations.
A µC is 10^-6 C.

a (1)

b(fk)

To find the Coulomb force on the +10 µC point charge due to the +4 µC charge, we will use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

(a) Expressing the Coulomb force in vector notation:
Let's assume the +10 µC charge is q1 and the +4 µC charge is q2.

The electric force between q1 and q2 can be calculated using the formula:

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

Here, F represents the force, k is the Coulomb constant (k = 9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Given:
q1 = +10 µC = 10 * 10^(-6) C
q2 = +4 µC = 4 * 10^(-6) C
r = distance between the charges

The vector notation for the force can be represented as:

F = (F_x)i + (F_y)j

To find the x and y components of the force, we need to break down the force into its horizontal and vertical components.

The x component of the force, F_x, is given by:
F_x = F * cos(angle)

Similarly, the y component of the force, F_y, is given by:
F_y = F * sin(angle)

We will calculate the angle between the two charges as well:

angle = tan^(-1)(y/x)

(b) Finding the magnitude of the force:
The magnitude of the force can be calculated using the Pythagorean theorem based on the x and y components:

Magnitude F = sqrt(F_x^2 + F_y^2)

Let's substitute the given values into the equations to find the Coulomb force in vector notation and its magnitude.