Find the total electric force on a +q charge placed at x_0 due to the line charge and the point charge
To find the total electric force on a +q charge placed at x_0 due to both a line charge and a point charge, you need to calculate the electric force separately for each source and then add them together.
1. Electric Force due to Line Charge:
The electric force on the +q charge due to the line charge can be obtained using the concept of electric field. First, we need to calculate the electric field at x_0 due to the line charge, and then multiply it by the charge q to get the force.
a. Calculate the electric field (E) at x_0 due to the line charge using the formula:
E = λ / (2πε₀x_0)
Here, λ is the linear charge density (charge per unit length) of the line charge, ε₀ is the permittivity of free space, and x_0 is the distance of the +q charge from the line charge.
b. Multiply the electric field (E) by the charge q to obtain the electric force (F_line) due to the line charge:
F_line = E × q
2. Electric Force due to Point Charge:
The electric force on the +q charge due to the point charge can be calculated using Coulomb's Law.
a. Calculate the electric field (E_point) at x_0 due to the point charge using the formula:
E_point = k × (q_point / r²)
Here, k is the electrostatic constant (k = 1 / (4πε₀)), q_point is the charge on the point charge, and r is the distance between the point charge and the +q charge.
b. Multiply the electric field (E_point) by the charge q to obtain the electric force (F_point) due to the point charge:
F_point = E_point × q
3. Total Electric Force:
The total electric force (F_total) on the +q charge at x_0 is the vector sum of the forces due to the line charge and the point charge:
F_total = F_line + F_point
By following these steps and using the appropriate formulas, you can calculate the total electric force on the +q charge placed at x_0 due to both the line charge and the point charge.