Finding the Electric Force on a Charge

Given Information:

- Charge 1: q1 = √3 × 10^-19 C
- Charge 2: q2 = -10^-6 C
- Position of Charge 1: (0,0,0)
- Position of Charge 2: (1,1,1)

To find the electric force on Charge 2, we will use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Coulomb's Law:

F = k * |q1| * |q2| / r^2

where F is the magnitude of the electric force, k is Coulomb's constant (9 × 10^9 N·m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

Calculating the Distance between Charges

To apply Coulomb's Law, we first need to find the distance between the charges. We can use the distance formula to find the distance between two points in three-dimensional space.

Distance Formula:

d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

where d is the distance between the points (x1, y1, z1) and (x2, y2, z2).

In this case, the points are (0,0,0) and (1,1,1), so we have:

d = √((1 - 0)^2 + (1 - 0)^2 + (1 - 0)^2)
d = √3

So the distance between the charges is √3 meters.

Calculating the Electric Force

Now we can use Coulomb's Law to find the electric force on Charge 2.

F = k * |q1| * |q2| / r^2

F = (9 × 10^9 N·m^2/C^2) * (√3 × 10^-19 C) * (10^-6 C) / (√3)^2

F = (9 × 10^9 N·m^2/C^2) * (√3 × 10^-19 C) * (10^-6 C) / 3

F = 3 × 10^-7 N

So the magnitude of the electric force on Charge 2 is 3 × 10^-7 N. But we also need to find the direction of the force, which is a vector quantity.

The direction of the force is along the line connecting the two charges and is repulsive since the charges have opposite signs. We can find the direction of the force using unit vectors.

Unit Vector:

A unit vector is a vector with a magnitude of 1 that points in a particular direction. We can find the unit vector in the direction of the line between two points by subtracting the position vectors of the two points and dividing by the distance between them.

In this case, the position vector of Charge 1 is (0,0,0) and the position vector of Charge 2 is (1,1,1). So we have:

u = (r2 - r1