Two particles with charges +2q and +q are separated by a distance r. The +2q particle has an electric field E at distance r and exerts a force F on the +q particle. What is the electric field of the +q particle at the same distance and what force does it exert on the +2q particle?

Question

Two particles with charges +2q and +q are separated by a distance r. The +2q particle has an electric field E at distance r and exerts a force F on the +q particle. What is the electric field of the +q particle at the same distance and what force does it exert on the +2q particle?

I think it should be E/2, F/2 but that's wrong. What should it be?

Answer 1

Newton's third Law !!!!

force of A on B = force of B on A

but anyway
distance R from 2Q
E = 2 k Q/R^2
F = E Q = 2 k Q^2/R^2

distance R from Q
E = k Q /R^2 half so agree
F = k 2Q Q /R^2 but the same force because half the field but twice the charge

Answer 2

To determine the electric field of the +q particle at the same distance r, we need to consider the principle of superposition. This principle states that the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.

Let's begin by calculating the electric field E1 at distance r due to the +2q particle. The electric field at a distance r from a point charge q is given by the equation:

E = k * |q| / r^2

where k is the Coulomb's constant (k ≈ 9 × 10^9 N m^2/C^2) and |q| is the absolute value of the charge. Plugging in the given values, the electric field E1 at distance r due to the +2q particle is:

E1 = k * (2q) / r^2

Now, let's consider the electric field E2 at distance r due to the +q particle. Following the same formula, the electric field E2 at distance r caused by the +q particle is:

E2 = k * (q) / r^2

The electric fields E1 and E2 are in the same direction since both charges are positive. Therefore, to find the total electric field at distance r, we need to sum the electric fields E1 and E2:

E_total = E1 + E2

E_total = k * (2q) / r^2 + k * (q) / r^2

E_total = k * (3q) / r^2

Thus, the electric field of the +q particle at the same distance r is E_total = k * (3q) / r^2.

Now, let's determine the force F2 exerted by the +q particle on the +2q particle. According to Coulomb's law, the force between two point charges is given by:

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

In this case, the force F2 exerted by the +q particle on the +2q particle is:

F2 = k * (q) * (2q) / r^2

F2 = 2k * (q^2) / r^2

Therefore, the electric field of the +q particle at the same distance is E_total = k * (3q) / r^2, and the force it exerts on the +2q particle is F2 = 2k * (q^2) / r^2.