H2 Physics 14 - Electric Fields: Force and Potential Between Point Charges

Step 1 - State the problem

Two point charges are placed thirty centimetres apart in a vacuum.

Step 1 - State the problem

Charge A is plus four microcoulombs and charge B is minus two microcoulombs.

Step 1 - State the problem

We want to find the electrostatic force between them, and the electric potential at the midpoint.

Step 2 - Calculate the electrostatic force using Coulomb's law

Coulomb's law says the force F equals one over four pi epsilon nought times the product of the magnitudes of the charges divided by r squared.

Step 2 - Calculate the electrostatic force using Coulomb's law

Substituting: F equals eight point nine nine times ten to the nine, times four times ten to the minus six, times two times ten to the minus six, all divided by zero point three zero squared.

Step 2 - Calculate the electrostatic force using Coulomb's law

The numerator is seven point one nine times ten to the minus two and the denominator is zero point zero nine.

Step 3 - Evaluate the force

Computing: F equals seven point one nine times ten to the minus two divided by nine times ten to the minus two.

Step 3 - Evaluate the force

That gives F approximately zero point eight zero newtons.

Step 3 - Evaluate the force

Since the charges have opposite signs, the force is attractive.

Step 4 - Find the electric potential at the midpoint

The midpoint is fifteen centimetres from each charge.

Step 4 - Find the electric potential at the midpoint

Electric potential is a scalar, so we add the contributions algebraically, not as vectors.

Step 4 - Find the electric potential at the midpoint

The potential at the midpoint V equals one over four pi epsilon nought times Q A over r A plus one over four pi epsilon nought times Q B over r B.

Step 5 - Evaluate the potential and state key takeaways

Inside the bracket: four micro divided by zero point one five gives two point six seven times ten to the minus five, and minus two micro divided by zero point one five gives minus one point three three times ten to the minus five.

Step 5 - Evaluate the potential and state key takeaways

Adding gives one point three three times ten to the minus five.

Step 5 - Evaluate the potential and state key takeaways

Multiply by eight point nine nine times ten to the nine to get V approximately one point two zero times ten to the five volts, or one hundred and twenty kilovolts.

Step 5 - Evaluate the potential and state key takeaways

Remember: potential is a scalar so positive and negative contributions can partially cancel, but the electric field at the midpoint is a vector and both contributions point in the same direction, from A towards B.