In an external electric field, the change in potential energy of a point charge q when it moves from point P to another point Q depends on:

A. The path taken by the charged particle

B. The magnitude of electric field

C. The direction of electric field

D. The shortest distance between point P and point Q

CONCEPT:

•  Force one a charge q in an electric field is defined as 

⇒ F = Eq

• The work done by this force in moving the charge by a distance d along the direction of electrostatic force (along the electric field) is

⇒ W = F.d = Eq.d

• The work done by external force in moving this charge by a distance d along the direction of the electrostatic field is

⇒ Wext = - W = - Eq.d

• By definition, the change in potential energy in moving the charge in an electrostatic field is equal to the work done by external forces

\(\Rightarrow \bigtriangleup U = W_{ext} = -Eq.d\)

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field

\(\Rightarrow V=\frac{W_{ext}}{q}\)

• Therefore the relation between electric potential and electric potential energy is given by

\(\Rightarrow \bigtriangleup U = W_{ext} = Vq\)

EXPLANATION:

• The change in potential energy is 

\(\Rightarrow \bigtriangleup U = W_{ext} = -Eq.d\)

Here, E is the electric field vector, and d is the shortest distance between points P and Q

• From the above equation, it is clear that the change in potential energy of a point charge q when it moves from point P to another point Q depends on
  • The magnitude of the electric field
  • The direction of the electric field
  • The shortest distance between point P and point Q
• Therefore option 2 is correct