In this lecture, we introduce the important concept of Electric Potential and understand its relationship with the Electric Field through potential gradient.

⚡ What is Electric Potential?

Electric potential at a point is defined as:

The work done per unit positive test charge in bringing it from infinity to that point against the electric field.

Mathematically:

V=WqV = \frac{W}{q}V=qW​

where:

• $V$ = electric potential

• $W$ = work done

• $q$ = test charge

🔹 Work Done in Bringing a Charge from Infinity

When a test charge is brought from infinity to a point near a charge $Q$, work has to be done against the electrostatic force.

The electric potential due to a point charge is:

V=kQrV = k \frac{Q}{r}V=krQ​

where:

• $Q$ = source charge

• $r$ = distance from the charge

• k=14πε0k = \frac{1}{4\pi \varepsilon_0}k=4πε0​1​

Important points:

• Potential is a scalar quantity

• SI unit → Volt (V)

• 1 Volt = 1 Joule per Coulomb

📉 Potential Gradient

Potential gradient is defined as:

The rate of decrease of electric potential with distance in the direction of the electric field.

Mathematically:

E=−dVdrE = -\frac{dV}{dr}E=−drdV​

This shows:

• Electric field is equal to the negative gradient of potential

• Potential decreases in the direction of the electric field

📌 Key Concepts Covered:

• Difference between electric field and electric potential

• Relation between work, charge, and potential

• Graphical interpretation of potential vs distance

• Connection between potential gradient and electric field strength

By the end of this lecture, you will clearly understand electric potential, calculate work done in moving a charge, and explain the concept of potential gradient with confidence.