Definition

The electric potential difference between two points is the work done to move a unit positive charge from one point to another while keeping the charge in electrostatic equilibrium.

Explanation

Consider two oppositely charged parallel plates with a unit positive Charge $+q_0$ placed between them.

a) Movement from Positive Plate to Negative Plate

• The charge $+q_0$ moves freely along the electric field lines toward the negative plate, driven by electric force.
• During this movement, the charge gains an equivalent amount of kinetic energy.

b) Movement from Negative Plate to Positive Plate

• To move $+q_0$ against the direction of the Electric Field, an external force equal and opposite to $\vec{F} = q_0\vec{E}$ must be applied.
• This keeps the charge in electrostatic equilibrium, enabling it to move at a uniform velocity without acceleration.

c) Work Done on the Charge

If:

• Potential energy at point $A = U_A$
• Potential energy at point $B = U_B$
• Work done to move the charge from $B$ to $A = W_{BA}$

Then:

$$U_A - U_B = W_{BA} \quad \text{or} \quad \Delta U = W_{BA}$$

Dividing both sides by $q_0$:

$$\frac{\Delta U}{q_0} = \frac{W_{BA}}{q_0}$$

The electric potential difference $\Delta V$ is defined as the work done per unit charge:

$$\Delta V = \frac{W_{BA}}{q_0}$$

Physical Significance

• Determines the direction of flow for positive charges.
• Positive charges always move from higher potential to lower potential.

Nature and Units

• Electric potential difference is a scalar quantity.
• SI unit: volt (V), where:

$$1 \, \text{volt} = \frac{1 \, \text{joule}}{1 \, \text{coulomb}}$$

• Multiples and submultiples of volt include:
  • $1 \, \mathrm{mV} = 10^{-3} \, \mathrm{V}$
  • $1 \, \mu\mathrm{V} = 10^{-6} \, \mathrm{V}$
  • $1 \, \mathrm{kV} = 10^{3} \, \mathrm{V}$
  • $1 \, \mathrm{MV} = 10^{6} \, \mathrm{V}$
  • $1 \, \mathrm{GV} = 10^{9} \, \mathrm{V}$

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Electric Potential

a) Definition

Electric potential at a point is the work done in bringing a unit positive charge from infinity to that point without any acceleration.

b) Explanation

From the potential difference formula:

$$\Delta V = \frac{W_{BA}}{q_0} \quad \text{or} \quad V_A - V_B = \frac{W_{BA}}{q_0}$$

If point $B$ is at infinity:

$$V_B = V_\infty = 0$$

Then:

$$V_A - 0 = \frac{W_{\infty A}}{q_0} \quad \text{or} \quad V_A = \frac{W_{\infty A}}{q_0}$$

Thus, the absolute electric potential at a point is:

$$V = \frac{W}{q_0}$$

Where $V$ is the electric potential, and $W$ is the work done.

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Summary

Concept	Definition	Key Formula
Electric Potential Difference	Work done to move a unit positive charge between two points in electrostatic equilibrium.	$\Delta V = \frac{W_{BA}}{q_0}$
Electric Potential	Work done to bring a unit positive charge from infinity to a specific point without acceleration.	$V = \frac{W}{q_0}$
Units	SI unit is volt (V). Other units include millivolts, kilovolts, etc.	$1 \, \text{volt} = \frac{1 \, \text{joule}}{1 \, \text{coulomb}}$

Significance

Understanding electric potential and potential difference is essential in analyzing electric circuits, fields, and energy transformations, enabling practical applications like batteries, capacitors, and electric power systems.

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References