Difference Between Electric Potential and Electric Field
Physics · Electrostatic Potential And Capacitance · NEET
Electric field (E) is a vector — it is the force per unit charge (N/C) and shows the direction of push on a charge. Electric potential (V) is a scalar — it is the potential energy per unit charge (volt) and has only a value, no direction. They are linked by E = -dV/dr, so the field points from high potential to low potential. Memory hook: "Field is a PUSH (vector), Potential is a PRICE (scalar) — the push always rolls charge downhill from high price to low price."
Potential V (blue curve) falls with distance; the electric field E (red arrows, a vector) points in the direction of decreasing potential. The field is the negative slope of the V curve: E = -dV/dr. Where V is flat, E = 0.
Your doubts, answered
Are electric field and electric potential the same thing?
No. Electric field E is force per unit charge (unit N/C or V/m) and is a vector, so it has direction. Electric potential V is potential energy per unit charge (unit volt) and is a scalar, so it has only magnitude. One tells you the force; the other tells you the energy.
Can electric potential be zero at a point where the electric field is NOT zero?
Yes. At the exact centre between two equal and opposite charges (or on the equatorial line of a dipole), the two potentials cancel to V = 0, but the field vectors add up and E is not zero. So V = 0 does not mean E = 0.
Can electric field be zero where the potential is NOT zero?
Yes. Inside a charged hollow conductor or shell the field is zero everywhere, yet the potential is a constant non-zero value (equal to the surface value). This is exactly the NEET 2024 shell PYQ: field zero, so potential is the same inside, giving zero potential difference.
What is the exact relation between E and V?
E = -dV/dr. The field equals the negative rate of change (gradient) of potential with distance. The minus sign means the field points in the direction of decreasing potential — from high V to low V.
Does a high potential always mean a strong field?
No. Potential depends on the value of V, field depends on how fast V changes. Where V is large but flat (dV/dr = 0), the field is zero. Field is about the slope of V, not the height of V.
⚠️ The NEET trap ✗ Students see V = 0 at a point and immediately write E = 0 there (or see E = 0 and write V = 0). ✓ V and E are independent quantities linked only by E = -dV/dr. V can be zero while E is large (dipole centre), and E can be zero while V is a non-zero constant (inside a shell). Check each one separately. 🧠 Zero potential does not mean zero field. Zero field does not mean zero potential. Slope, not height.
Real NEET questions
NEET 2023 (Phase 2)
A conducting sphere of radius R is charged. The electric field at a distance r (r > R) from the centre of the sphere is (V = potential on the surface of the sphere):
A · RV/r² ✓
B · V/r
C · rV/R²
D · R²V/r³
Solution: Step 1: Surface potential of the sphere: V = kQ/R, where k = 1/(4πε₀). Step 2: Rearrange to get kQ = RV. Step 3: A charged sphere acts like a point charge for outside points, so field at r > R is E = kQ/r². Step 4: Substitute kQ = RV: E = RV/r². This shows E and V are different — you must convert V to charge first, then find the field. Answer: A.
NEET 2024
A thin spherical shell is charged by some source. The potential difference between two points C and P (both inside the shell) is (Take 1/4πε₀ = 9 × 10⁹ SI units):
A · 1 × 10⁵ V
B · 0.5 × 10⁵ V
C · Zero ✓
D · 3 × 10⁵ V
Solution: Step 1: All charge sits on the shell surface, so the electric field inside the shell is E = 0 everywhere. Step 2: Since E = -dV/dr and E = 0, dV/dr = 0, meaning V does not change inside. Step 3: Therefore every interior point has the same potential. Step 4: Points C and P are both inside, so ΔV = V_C - V_P = 0. Note E = 0 but V itself is a non-zero constant — the classic field-vs-potential trap. Answer: C.
Solved Electrostatic Potential And Capacitance NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Electric potential (V) is a scalar — only magnitude, in volts. Electric field (E) is a vector — magnitude and direction, in N/C or V/m.
What are the SI units of E and V?
Electric field: newton per coulomb (N/C), which is the same as volt per metre (V/m). Electric potential: volt (V), which is joule per coulomb (J/C).
How do you get E from V and V from E?
To get field from potential, differentiate: E = -dV/dr. To get potential from field, integrate: V = -∫E·dr. So field is the slope of the potential graph.
Why does the field point from high to low potential?
Because of the minus sign in E = -dV/dr. A positive charge naturally moves to lower potential energy, and the field defines the direction of force on a positive charge, so it points down the potential slope.
Which quantity is used to find work done, E or V?
Use potential. Work done in moving charge q between two points is W = q(V_A - V_B) = qΔV. It does not depend on the path, only on the potential difference between the two points.
