Electric Potential Energy

• In order to move a positive charge closer to another positive charge, work must be done to overcome the force of repulsion between them
  • Similarly, to move a positive charge away from a negative charge, work must be done to overcome the force of attraction between them

   

• Energy is therefore transferred to the charge that is being pushed upon
  • This means its?potential energy?increases

   

• If the positive charge is free to move, it will start to move away from the repelling charge
  • As a result, its potential energy decreases back to 0

   

• This is analogous to the gravitational potential energy of a mass increasing as it is being lifted upwards and decreasing as it falls
• The electric potential at a point is defined as:

The work done per unit charge in bringing a positive test charge from infinity to that point

• Electric potential is a?scalar?quantity
  • This means it doesn’t have a direction

   

• However, you will still see the electric potential with a positive or negative sign. This is because the electric potential is:
  • Positive?around an isolated positive charge
  • Negative?around an isolated negative charge
  • Zero?at infinity

   

• Positive work is done to move a positive test charge from infinity to a point around a positive charge and negative work is done to move it to a point around a negative charge. This means:
  • When a positive?test charge?moves closer to a?negative?charge, its electric potential?decreases
  • When a positive test charge moves closer to a?positive?charge, its electric potential?increases

The electric potential V decreases in the direction the test charge would naturally move in due to repulsion or attraction

Electric Potential due to a Point Charge

• The?electric potential?in the radial field due to a?point charge?is defined as:

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

   

• This equation shows that for a positive test charge:
  • As the distance?r?from the charge?Q?decreases, the potential?V?increases?(becomes more positive)
  • This is because more work has to be done on the positive test charge to overcome the repulsive force of?Q

   

• For a negative test charge:
  • As the distance from the charge?r?decreases, the potential?V?decreases?(becomes more negative)
  • This is because less work has to be done on the negative test charge since the attractive force becomes stronger the nearer it gets to?Q

   

• Unlike the?gravitational potential?equation, the electric potential can be positive or negative, because?Q?can be positive or negative
• The electric?potential?varies according to 1 / r
  • Note, this is different to electric?field?strength, which varies according to 1 / r2

Step 1: Write the equation for electric potential

• • The electric potential is given by the equation:

Step 2: Write the transformed equation for a distance three times as large

• • The charge?Q?remains constant (due to the proton)
  • The potential?V?becomes?V'
  • The distance?r?becomes 3r
  • Hence the transformed equation becomes:

Step 3: Write a conclusion

• • Therefore, when the distance from a charge?Q?gets three times larger, the value of the electric potential decreases by a factor 1/3, because the potential is inversely proportional to distance?r