Two identical point charges (q 7.20 106 C) are fixed at diagonally opposite corners of a

Question

Two identical point charges

(q 7.20 106 C) are fixed at

diagonally opposite corners of a

square with sides of length 0.480 m.

A test charge (q02.40 108 C),

with a mass of 6.60 108 kg, is

released from rest at one of the empty corners of the square. Determine

the speed of the test charge when it reaches the center of the square.

IN YOUR ANSWER PLEASE EXPLAIN WHY ONE r=.48m AND WHY THE OTHER IS r=.34m.

Answer 1

I would solve this using energy.

First, find the potential energy between the "test charge" and the combined pull** from the other 2.

The coulomb force is F = kq₁ * q₂ / r²

You are given the dimensions of the square. Find the force due to each charge, and then the vector sum of the 2. The result is a force between the test charge, and an equivalent single charge at the center of the diagonal (the point at which the coulomb force would drop to zero)

Once you have the potential energy (PE), recognize that--when the test charge reaches the center--all of the PE will be converted to kinetic energy (KE).

KE = 1/2 * m * v²

You have KE = PE, and you are given the mass of the test charge, so you can now solve for v.