Two charges, -15 and +4.5 µC, are fixed in place and separated by 2.8 m. At what spot along a line through the charges is the net electric field zero? What would be the force on a charge of +1 µC placed at this spot?
To find the spot along the line between the charges where the net electric field is zero, we can use the principle of superposition. The net electric field is the vector sum of the electric fields created by each individual charge.
The electric field created by a point charge can be calculated using the formula:
Electric field (E) = (k * q) / r^2
where k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), q is the charge of the point charge, and r is the distance between the point charge and the spot where we want to find the net electric field.
Let's denote the positive charge as "q1" and the negative charge as "q2". The electric field due to q1 at the spot along the line is directed away from it, while the electric field due to q2 is directed towards it. For the net electric field to be zero, the magnitudes of the electric fields due to q1 and q2 should be equal.
So, we can set up the following equation:
(E1) = (E2)
(k * q1) / r1^2 = (k * q2) / r2^2
Where r1 is the distance between q1 and the spot, and r2 is the distance between q2 and the spot.
Given the charges q1 = -15 µC and q2 = +4.5 µC, and the separation distance d = 2.8 m, we need to solve for r1 and r2.
Using the properties of the line that passes through q1 and q2, we have r1 + r2 = d.
Solving the system of equations, we can calculate r1 and r2. The values of r1 and r2 would give us the distances from the spot to q1 and q2, respectively, where the net electric field is zero.
Once we find the spot, we can calculate the force on a charge of +1 µC placed at that spot using the formula:
Force = (k * q1 * q3) / r^2
where q3 is the charge we placed and r is the distance between the charge and the spot. Substituting the values, we can find the force.
Hence, we need to calculate r1 and r2 using the equations described above and then find the force on a charge of +1 µC using the formula mentioned.