Electric Potential and Energy

Electric Potential

• Definition: Electric potential energy (U) is the work needed to bring a positive unit charge from infinity to a point in an electric field.

Gravitational Potential Energy

• Formula: $GPE = mg riangle h$ Where:
  • $m$ = mass
  • $g$ = acceleration due to gravity
  • $riangle h = h<em>A - h</em>B$
• The work required to change gravitational potential is defined as:
  $W = (F_{gravity})( riangle h)$
• Example: Lifting a book against the force of gravity.

Electric Potential Energy

• Protons & Electric Forces:
  • A proton at rest at point A may have different potential energy compared to point B.
  • Change in electric potential energy:
    $riangle PE<em>e = q</em>o E riangle d$
  • Work done when moving between two points:
    $-W<em>{E(AB)} = q</em>o E riangle d$
• Work: It takes positive work to separate unlike charges, and negative work to bring like charges closer.

Electric Potential (V)

• Definition: Electric potential is the potential energy per unit charge expressed as:
  V = rac{U}{q_o}
• Units:
  • SI unit of Electric Potential is Volt (V).
  • 1 V = rac{1 J}{C} (1 Joule per Coulomb)

Relationship with Electric Field

• The relationship between work done by electric force from A to B using voltage (potential difference):
  $W<em>{A ightarrow B} = U</em>B - U<em>A = - (V</em>B - V_A)$
• Potential Difference: Also known as voltage, it represents energy per unit charge.

Electric Fields and Potential

• Electric field (E) can be expressed as: $V = E imes d$ Where:
  • Fed into the formula for practical applications involving plates or capacitors.

Capacitors

• Two parallel plates create a uniform electric field where the force remains constant.
• The work done in moving a test charge (q) through an electric field:
  $W<em>{AB} = q</em>o E d$.

Examples of Electric Potential

1. Example 1: To find the potential difference (V) when moving 2.5mC of charge with energy of 1.00 x 10^-3 Joules:
   V = rac{W}{q_o} = rac{1.00 imes 10^{-3}}{2.5 imes 10^{-3}} = 400V

2. Example 2: For a spark plug with plates separated by 0.50 mm and electric field of 4.8 x 10^7 V/m:
   $V = E imes d = (4.8 imes 10^7) imes (0.50 imes 10^{-3}) = 24,000 V$

3. Example 3: For a potential difference of 600V between oppositely charged plates:

   • Electric Field Strength:
     E = rac{V}{d}
   • Force on an electron:
     $F = qE$

Equipotential Lines

• Equipotential lines show locations where electric potential is constant; represent surfaces where charges can move without work.
• They are perpendicular to electric field lines.

Key Concepts Review

• Electric potential energy defines the work needed to move charges in a field.
• Electric potential (voltage) represents energy per charge and remains constant regardless of the path taken.
• Work done in a uniform electric field can be calculated easily by knowing charge and electric field.
• Electric field and equipotential lines have a defined relationship and influence the behavior of charges and energy in systems.