# 7.4.6 Radial Electric Field

### Electric Field of a Point Charge

• The electric field strength describes how strong or weak an electric field is at that point
• A point charge produces a radial field
• A charge sphere also acts like a point charge
• The electric field strength E at a distance r due to a point charge Q in free space is defined by:

• Where:
• Q = the point charge producing the radial electric field (C)
• r = distance from the centre of the charge (m)
• ε0 = permittivity of free space (F m-1)

• This equation shows:
• Electric field strength in a radial field is not constant
• As the distance from the charge r increases, E decreases by a factor of 1/r2

• This is an inverse square law relationship with distance
• This means the field strength E decreases by a factor of four when the distance r is doubled
• Note: this equation is only for the field strength around a point charge since it produces a radial field

• The electric field strength is a vector Its direction is the same as the electric field lines
• If the charge is negative, the E field strength is negative and points towards the centre of the charge
• If the charge is positive, the E field strength is positive and points away from the centre of the charge
• This equation is analogous to the gravitational field strength around a point mass

#### Worked Example

A metal sphere of diameter 15 cm is negatively charged. The electric field strength at the surface of the sphere is 1.5 × 105 V m-1.

Determine the total surface charge of the sphere.

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

Step 3: Rearrange for charge Q

Q = 4πε0Er2

Step 4: Substitute in values

Q = (4π × 8.85 × 10-12) × (1.5 × 105) × (7.5 × 10-2)2 = 9.38 × 10-8 C = 94 nC (2 s.f)

#### Exam Tip

Remember to always square the distance in the electric field strength equation!

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