Question

Object A has a charge q on it, object B has a charge q on it, and Object C has a charge 2q on it. These charges are arranged, one each, at the vertices of an equilateral triangle. Which charge has the greatest magnitude electric force on it?a. Ab. Bc. Cd. All have equal magnitude forces on them.

Answer 1

Answer: Option d.

Explanation:

The force between charges can be expressed as:

F = k*q1*q2/r^2

where k is a constant, q1 and q2 are the charges and r is the distance between them.

We hare in a equilateral triangle, so al the distances are equal.

and the charges are:

qa = q

qb = q

qc = 2q

Now, for example, the force that experiments charge A is (in the y axis)

F = (k*qa*qb/r^2 + k*qa*qc/r^2)*cos(30°) = cos(30°)*(q + 2q)*k*q/r^2 = cos(30°)*3*k*q^2/r^2

for charge B, the force is again, in the y axis.

F = (k*qb*qa/r^2 + k*qb*qc/r^2)*cos(30°) = cos(30°)*(q + 2q)*k*q/r^2 = cos(30°)*3*k*q^2/r^2

for particle C, we have:

F = (k*qc*qa/r^2 + k*qc*qb/r^2)*cos(30°) = cos(30°)*(q + q)*k*2q/r^2 = cos(30°)*4*k*q^2/r^2

Wher the cosine of 30° comes because we have a equilatiral triangle, where all the internal angles are 60°, so if we draw a line that cuts the angle by half (our y-axis) the angles to each side are 30°.

We can do a similar process for the forces in the x-axis, and we will reach the same conclusion:

Now, this means that the force that experiences the charge C is the biggest force, so the correct option is c.