19.2 Electric Potential in a Uniform Electric Field

Electric potential in a uniform field is all about the relationship between voltage and electric field strength. The key equation is V = Ed, where V is voltage, E is field strength, and d is distance between points in the field.

This concept helps us understand how voltage changes with distance in a uniform field. We can use it to calculate voltage, field strength, or distance when given the other two variables. It's crucial for analyzing parallel plate capacitors and other uniform field setups.

Electric Potential in a Uniform Electric Field

Voltage and electric field relationship

Top images from around the web for Voltage and electric field relationship

• 

  19.4 Equipotential Lines – College Physics View original

  Is this image relevant?

• 

  File:Parallel plate capacitor.svg - Wikipedia View original

  Is this image relevant?

• 

  Electric Potential in a Uniform Electric Field | Physics View original

  Is this image relevant?

• 

  19.4 Equipotential Lines – College Physics View original

  Is this image relevant?

• 

  File:Parallel plate capacitor.svg - Wikipedia View original

  Is this image relevant?

1 of 3

Top images from around the web for Voltage and electric field relationship

• 

  19.4 Equipotential Lines – College Physics View original

  Is this image relevant?

• 

  File:Parallel plate capacitor.svg - Wikipedia View original

  Is this image relevant?

• 

  Electric Potential in a Uniform Electric Field | Physics View original

  Is this image relevant?

• 

  19.4 Equipotential Lines – College Physics View original

  Is this image relevant?

• 

  File:Parallel plate capacitor.svg - Wikipedia View original

  Is this image relevant?

1 of 3

• Voltage or electric potential difference directly proportional to electric field strength in uniform field
  • Relationship given by equation: $V = Ed$
    • $V$ voltage or electric potential difference
    • $E$ electric field strength
    • $d$ distance between two points in field
• Electric field constant in magnitude and direction throughout uniform field
• As distance between two points increases, voltage between them increases linearly, given constant electric field strength (parallel plate capacitor)

Expressions for potential and field

• Electric potential difference (voltage) in uniform field:
  • $V = Ed$
    • Derived from work done by electric field on test charge moved between two points
    • Work done equal to change in potential energy: $W = qEd = q(V_f - V_i)$
    • Rearranging equation yields: $V_f - V_i = Ed$, where $V_f - V_i$ voltage
• Electric field strength in uniform field:
  • $E = \frac{V}{d}$
    • Obtained by rearranging equation $V = Ed$
    • Electric field strength voltage divided by distance between two points (electric field lines)

Energy and work in electric fields

• Potential energy in an electric field is related to the work done by the field
• Work done by the electric field is equal to the negative change in potential energy
• Conservation of energy applies to charges moving in electric fields
• Equipotential surfaces are perpendicular to electric field lines
• Electric dipoles experience torque in uniform electric fields due to potential energy differences

Calculations in uniform fields

• Use equation $V = Ed$ to solve problems involving any two of three variables
  1. If given voltage and distance, calculate electric field strength: $E = \frac{V}{d}$
  2. If given electric field strength and distance, calculate voltage: $V = Ed$
  3. If given voltage and electric field strength, calculate distance: $d = \frac{V}{E}$
• Pay attention to units when solving problems
  • Electric field strength typically measured in V/m or N/C
  • Voltage measured in V
  • Distance usually measured in m (uniform field between charged plates)
• When solving problems, identify given variables and unknown variable, then use appropriate equation to solve for unknown