# 21.1.3 Electric Field Strength

### Electric Field of a Point Charge

• The electric field strength at a point describes how strong or weak an electric field is at that point
• The electric field strength E at a distance r due to a point charge Q in free space is defined by: • Where:
• Q = the charge producing the 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 is not constant
• As electric field strength increases, decreases by a factor of 1/r2
• This is an inverse square law relationship with distance
• This means the field strength decreases by a factor of four when the distance 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

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! ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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