• The?electric potential?in the field due to a?point charge?is defined as:Where:
  • V?= the electric potential (V)
  • Q?= the point charge producing the potential (C)
  • ε0?=?permittivity of free space?(F m-1)
  • r?= distance from the centre of the point charge (m)

• This equation shows that for a positive (+) charge:
  • As the distance from the charge?r?decreases, the potential?V?increases
  • This is because more work has to be done on a positive test charge to overcome the repulsive force
• For a negative (?) charge:
  • As the distance from the charge?r?decreases, the potential?V?decreases
  • This is because less work has to be done on a positive test charge thanks to the effect of the attractive force
• Unlike the?gravitational potential?equation, the minus sign in the electric potential equation will be included in the charge
• The electric potential changes according to an?inverse square law?with distance

The potential changes as an inverse law with distance near a charged sphere

• Note:?this equation still applies to a conducting sphere. The charge on the sphere is treated as if it concentrated at a point in the sphere from the point charge approximation

Part (a)

Step 1: Write down the known quantities

• • • Radius of the dome,?r?= 15 cm = 15 × 10-2?m
    • Potential difference,?V?= 240 kV = 240 × 103?V

Step 2: Write down the equation for the electric potential due to a point chargePart (b)

Step 1: Write down the known quantities

• • Q?= charge stored in the dome = 4.0 μC = 4.0 × 10-6?C
  • r?= radius of the dome + distance from the dome = 15 + 30 = 45 cm = 45 × 10-2?m

Step 2: Write down the equation for electric potential due to a point chargeWorked Example

Step 1: Write down the known values

• • Electric field strength,?E?= 1.5 × 105?V m-1
  • Radius of sphere,?r?= 15 / 2 = 7.5 cm = 7.5 × 10-2?m

Step 2: Write out the equation for electric field strength