Physics

Problem

Two point charges are fixed on the

x

-axis:

+6.0\,\mu\text{C}

x=0

and

+2.0\,\mu\text{C}

x=0.30\,\text{m}

. Take the positive

x

-direction as positive electric field direction. (a) Write the mathematical expression for the magnitude of the electric field due to a single point charge at a distance

r

. (b) Calculate the magnitude and direction of the net electric field at the point

P

located at

x=0.15\,\text{m}

. (c) Determine the position(s) on the

x

-axis, other than at infinity, where the net electric field due to the two charges becomes zero. Express your answer as a distance from the charge at the origin.

Intuitive explanation

PART (A)

The electric field from a point charge is determined by Coulomb's law—it depends on the charge's magnitude and falls off with the square of distance. Just write down the standard formula that relates field strength to charge and distance.

PART (B)

At any point, the net field is the vector sum of fields from both charges. Since both charges are positive, each creates a field pointing away from itself; the key is recognizing that these fields point in opposite directions at

P

(which lies between the charges), so you subtract their magnitudes to find the net effect.

PART (C)

The net field is zero where the two fields cancel—they must be equal in magnitude but opposite in direction. Since both charges are positive, this can only happen on the

x

-axis outside the region between them, where the weaker charge's field can balance the stronger one's. Set up an equation equating the magnitudes and solve for the position.