# 18.1.3 Electric Field Strength

### Electric Field Strength

• Where:
• E = electric field strength (V m-1)
• ΔV = potential difference between the plates (V)
• Δd = separation between the plates (m)
• Note: the electric field strength is now also defined by the units V m-1
• The equation shows:
• The greater the voltage between the plates, the stronger the field
• The greater the separation between the plates, the weaker the field
• Remember this equation cannot be used to find the electric field strength around a point charge (since this would be a radial field)
• The direction of the electric field is from the plate connected to the positive terminal of the cell to the plate connected to the negative terminal
• Note: if one of the parallel plates is earthed, it has a voltage of 0 V

Step 1:            Write down the known values

Potential difference, ΔV = 7.9 kV = 7.9 × 103 V

Distance between plates, Δd = 3.5 cm = 3.5 × 10-2 m

Charge, Q = 2.6 × 10-15 C

Step 3:            Write out the equation for electric force on a charged particle

F = QE

Step 4:            Substitute electric field strength and charge into electric force equation

F = QE = (2.6 × 10-15) × (2.257 × 105) = 5.87 × 10-10 N = 5.9 × 10-10 N (2 s.f.)

### 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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