Electric Potential – Class 12 + JEE Main | Complete Concept

Electric Potential – Class 12 + JEE Main

Electric Potential Electrostatics ka ek extremely important concept hai. Electric field ke questions ke saath-saath JEE Main mein potential, potential difference, potential energy, equipotential surfaces aur conductor ke concepts par direct aur conceptual questions pooche ja sakte hain.

Electric field ko samajhne ke baad potential ko samajhna comparatively easy ho jaata hai. Sabse important difference yaad rakho: Electric Field ek vector quantity hai, jabki Electric Potential ek scalar quantity hai.

Is article mein hum electric potential ki definition se lekar point charge, multiple charges, electric field aur potential ka relation, potential energy, equipotential surfaces, conductors aur JEE Main application ko step-by-step cover karenge.

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1. Electric Potential

Kisi point par electric potential ko define kiya jaata hai as the work done per unit positive test charge in bringing that test charge from infinity to that point.

V = W / q₀

Yahan:

• V = electric potential
• W = work done
• q₀ = positive test charge

SI Unit

Electric potential ki SI unit Volt (V) hai.

1 Volt = 1 Joule/Coulomb

Nature of Electric Potential

Electric potential ek scalar quantity hai. Iska matlab hai ki potential ko add karne ke liye vector addition ki zarurat nahi hoti.

Isi scalar nature ki wajah se multiple charges ke potential ko solve karna electric field ke comparison mein kaafi simple hota hai.

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2. Electric Potential Difference

Do points A aur B ke beech potential difference ko work done per unit charge ke form mein express kiya ja sakta hai.

V_B − V_A = W_A→B / q

Yahan W_A→B ko given convention ke according external agent dwara kiya gaya work maana gaya hai.

Electric Field aur Potential ki Direction

Electric field ki direction higher potential se lower potential ki taraf hoti hai.

Higher V → Lower V

Is relation ko yaad rakhne ka simple idea hai: electric field potential ko decrease karne ki direction mein point karta hai.

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3. Potential Due to a Point Charge

Agar vacuum mein ek point charge Q placed hai aur kisi point ki us charge se distance r hai, toh us point par potential:

V = kQ/r

Jahan:

k = 1/(4πε₀) = 9 × 10⁹ N·m²/C²

Charge ka Sign Important Hai

Charge	Potential
Q > 0	V > 0
Q < 0	V < 0

Formula se clearly:

V ∝ Q

Aur distance ke respect mein:

V ∝ 1/r

Sabse important point: Potential scalar hai. Isliye isme direction nahi hoti aur multiple potentials ko algebraically add kiya ja sakta hai.

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4. Electric Potential Due to Multiple Charges

Jab system mein multiple point charges present hon, toh kisi point par total potential simply individual potentials ka algebraic sum hoga.

V_net = V₁ + V₂ + V₃ + ...

Therefore:

V_net = k(Q₁/r₁ + Q₂/r₂ + Q₃/r₃ + ...)

JEE Trick

Potential ke case mein vector addition nahi karni hoti.

Sirf har charge ka sign properly include karo aur potentials ko algebraically add kar do.

Example

Suppose kisi point se equal distance par +Q aur −Q charges hain.

Unke individual potentials equal magnitude aur opposite sign ke honge:

V₁ = kQ/r

V₂ = −kQ/r

Therefore:

V_net = 0

Ye result potential ke scalar nature ka direct application hai.

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5. Relation Between Electric Field and Potential

Electric field aur electric potential directly related hain.

E = −dV/dr

Uniform electric field ke case mein:

E = −ΔV/Δr

Negative Sign ka Meaning

Formula mein negative sign bahut important hai. Ye indicate karta hai ki electric field potential ke decreasing direction mein point karta hai.

Electric Field → Decreasing Potential ki Direction

Isi wajah se electric field ko higher potential se lower potential ki taraf directed maana jaata hai.

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6. Work Done and Potential

Agar charge q kisi potential V par present hai, toh uski electric potential energy:

U = qV

Yahan:

• U = electric potential energy
• q = charge
• V = electric potential

Work Done by Electric Field

Electric field conservative hota hai. Work done by electric field aur potential energy ke beech:

W_field = −ΔU

Since:

ΔU = q(V_B − V_A)

Therefore:

W_field = q(V_A − V_B)

Conservative Nature

Electric field conservative hone ka matlab hai ki electric field dwara kiya gaya work path par depend nahi karta.

Work sirf:

• Initial position
• Final position

par depend karta hai.

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7. Potential Energy of Two Charges

Do point charges q₁ aur q₂ agar distance r par separated hain, toh system ki potential energy:

U = kq₁q₂/r

Sign of Potential Energy

Charges	q1q2	Potential Energy
Like charges	Positive	U > 0
Unlike charges	Negative	U < 0

Therefore:

q₁q₂ > 0 → U positive

q₁q₂ < 0 → U negative

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8. Potential Energy of a System of Charges

Agar system mein multiple charges hain, toh total electrostatic potential energy ko har unique pair ke contribution ko add karke calculate kiya jaata hai.

U = k Σ(q_iq_j/r_ij)

Yahan summation mein every unique pair of charges consider kiya jaata hai.

Important JEE Point

Same pair ko twice count mat karo.

For example, agar charges hain: q₁, q₂, q₃, toh pairs honge:

• q₁q₂
• q₁q₃
• q₂q₃

q₁q₂ aur q₂q₁ ko separate pairs nahi maana jaata.

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9. Equipotential Surface

Aisi surface jahan har point par electric potential same hota hai, usse equipotential surface kehte hain.

V = constant

Isliye equipotential surface par:

ΔV = 0

Work Done on Equipotential Surface

Potential difference zero hai, therefore charge ko equipotential surface ke along move karne mein electric field dwara work:

W = qΔV = 0

Hence: Equipotential surface ke along charge move karne par work done zero hota hai.

Important Properties

• Equipotential surface par V constant hota hai.
• ΔV = 0.
• Surface ke along work done zero hota hai.
• Electric field equipotential surface ke perpendicular hota hai.
• Do equipotential surfaces intersect nahi karti.

Electric field agar equipotential surface ke along component rakhta, toh surface par potential change hota. Isliye electrostatic situation mein electric field surface ke normal direction mein hota hai.

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10. Important Result – Point Charge

Point charge ke liye:

V = kQ/r

Aur electric field magnitude:

E = kQ/r²

Potential ko differentiate karne par electric field ka relation milta hai:

E = −dV/dr

Isliye potential aur electric field ko completely separate concepts mat samjho. Dono electrostatic field ko describe karne ke closely related methods hain.

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11. Potential Due to an Infinite Line Charge

Infinite line charge ke case mein potential ka expression:

V = (λ / 2πε₀) ln(r₀/r)

Yahan:

• λ = linear charge density
• r = observation point ki line charge se distance
• r₀ = chosen reference distance

Important Concept

Infinite line charge ke case mein potential ko infinity par zero reference nahi kiya ja sakta. Isliye potential calculate karne ke liye ek reference distance r₀ choose ki jaati hai.

Ye point JEE Main mein conceptual trap ban sakta hai.

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12. Potential of a Conductor

Electrostatic equilibrium mein conductor ke andar electric field:

E = 0

Is condition ki wajah se conductor ke andar potential constant hota hai.

V = constant

Inside Conductor

Electrostatic equilibrium mein conductor ke andar:

E = 0

Aur potential everywhere constant hota hai.

Surface of Conductor

Conductor ki surface par bhi potential conductor ke potential ke equal hota hai.

Most Important Trap

E = 0 does NOT mean V = 0.

Iska actual meaning hai:

E = 0 → V is constant

Constant potential zero bhi ho sakta hai aur non-zero bhi.

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13. JEE Shortcut – Change in Potential

Point charge ke liye:

V = kQ/r

Is formula se proportionality immediately identify karo:

V ∝ Q/r

Case 1: Q becomes 2Q

Agar charge double kar diya:

V′ = k(2Q)/r = 2V

Case 2: r becomes 2r

V′ = kQ/(2r) = V/2

Case 3: Q becomes 2Q and r becomes 2r

V′ = k(2Q)/(2r)

V′ = V

Golden Rule:

V ∝ Q/r

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14. Solved JEE Main Question

Question

A charge:

Q = 2 μC

is placed in vacuum. Find the electric potential at:

r = 30 cm

Step 1: Convert Units

Charge:

2 μC = 2 × 10⁻⁶ C

Distance:

30 cm = 0.3 m

Step 2: Apply Formula

V = kQ/r

Substitute:

V = (9 × 10⁹ × 2 × 10⁻⁶)/0.3

Step 3: Calculate

V = (18 × 10³)/0.3

V = 6 × 10⁴ V

Final Answer

6 × 10⁴ V

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15. Common JEE Main Traps

Trap 1: Potential ko Vector Treat Karna

Electric field vector hai, lekin electric potential scalar hai. Multiple charges ke potential mein simple algebraic addition karo.

Trap 2: E = 0 ka Meaning V = 0 Samajhna

Ye incorrect hai.

E = 0 → V constant

Trap 3: Charge ka Sign Ignore Karna

Point charge ke liye:

V = kQ/r

Positive charge positive potential deta hai, while negative charge negative potential deta hai.

Trap 4: Distance ko Diameter Samajhna

Formula mein r charge aur observation point ke beech ki actual distance hai. Geometry question mein radius aur diameter ko carefully distinguish karo.

Trap 5: Equipotential Surface Par Work Non-Zero Lena

Equipotential surface par:

ΔV = 0

Therefore:

W = qΔV = 0

Trap 6: Infinite Line Charge ke Potential ko Infinity par Zero Karna

Infinite line charge ke liye potential ko infinity par zero reference nahi kiya ja sakta. Reference distance use karni padti hai.

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16. JEE Main Quick Solving Strategy

Electric Potential ka question dekhte hi pehle identify karo ki question kis category ka hai.

Question Type	Direct Approach
Single point charge	V = kQ/r
Multiple point charges	Vnet = ΣV
Charge in potential V	U = qV
Two charges	U = kq1q2/r
Potential change in space	E = −dV/dr
Uniform field	E = −ΔV/Δr
Equipotential surface	ΔV = 0 → W = 0
Conductor in electrostatic equilibrium	E = 0, V = constant

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17. Electric Potential Formula Sheet

Concept	Formula
Electric Potential	V = W/q0
Unit	Volt = Joule/Coulomb
Point Charge	V = kQ/r
Multiple Charges	Vnet = ΣV
Electric Field-Potential Relation	E = −dV/dr
Uniform Field	E = −ΔV/Δr
Potential Energy	U = qV
Two Charges	U = kq1q2/r
Work by Electric Field	Wfield = q(VA − VB)
Equipotential	ΔV = 0
Work on Equipotential	W = 0
Conductor	E = 0, V = constant
Infinite Line Charge	V = (λ/2πε0) ln(r0/r)

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18. Electric Potential vs Electric Field

Electric Potential	Electric Field
Scalar quantity	Vector quantity
Unit: Volt	Unit: N/C or V/m
V = kQ/r for point charge	E = kQ/r² for point charge
Potential can be algebraically added	Electric fields require vector addition
Related through E = −dV/dr	Points towards decreasing potential

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19. One-Minute Revision

Exam se just pehle Electric Potential revise karna ho, toh ye points yaad rakho:

1. V = W/q₀
2. Electric potential is a scalar quantity.
3. Unit = Volt.
4. 1 V = 1 J/C.
5. Point charge: V = kQ/r.
6. Positive Q → positive V.
7. Negative Q → negative V.
8. Multiple charges → algebraic addition.
9. E = −dV/dr.
10. Electric field points towards decreasing potential.
11. U = qV.
12. Two charges: U = kq₁q₂/r.
13. Electric field conservative hai.
14. Equipotential surface: ΔV = 0.
15. Equipotential surface ke along work = 0.
16. Electric field equipotential surface ke perpendicular hota hai.
17. Conductor ke inside electrostatic equilibrium mein E = 0.
18. E = 0 does not mean V = 0.
19. Conductor ke inside potential constant hota hai.

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20. Final Revision Box

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ELECTRIC POTENTIAL – MUST REMEMBER

Electric Potential:

V = W/q<sub>0</sub>

Point Charge:

V = kQ/r

Multiple Charges:

V<sub>net</sub> = ΣV

Electric Field:

E = −dV/dr

Potential Energy:

U = qV

Two Charges:

U = kq<sub>1</sub>q<sub>2</sub>/r

Work by Electric Field:

W<sub>field</sub> = q(V<sub>A</sub> − V<sub>B</sub>)

Equipotential:

ΔV = 0 → W = 0

Conductor:

E = 0 → V = constant

Most Important:

Electric Potential → Scalar

Electric Field → Vector

Direction:

Electric Field → Higher Potential to Lower Potential

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21. Practice Questions

1. A point charge of 5 μC is placed in vacuum. Find the potential at a distance of 20 cm.
2. Two equal and opposite charges are placed at equal distances from a point. Find the potential at that point.
3. What happens to electric potential if the charge is doubled while distance remains constant?
4. What happens to potential if both charge and distance are doubled?
5. Find the potential energy of two charges q₁ and q₂ separated by distance r.
6. A charge is moved along an equipotential surface. Find the work done by the electric field.
7. If E = 0 inside a conductor, what can you conclude about the potential?
8. Explain why electric field is perpendicular to an equipotential surface.
9. Why is potential due to multiple charges added algebraically rather than vectorially?
10. Why can infinity not be used as the zero-potential reference for an infinite line charge?

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22. PDF Notes

Electric Potential ke notes/PDF ko directly access karne ke liye neeche PDF embed section diya gaya hai.

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23. Frequently Asked Questions – Electric Potential

Q1. Electric potential scalar hai ya vector?

Electric potential ek scalar quantity hai. Isliye multiple charges ke potentials ko algebraically add kiya jaata hai.

Q2. Point charge ke due potential ka formula kya hai?

Point charge Q se distance r par: V = kQ/r.

Q3. Electric field aur potential ka relation kya hai?

Electric field aur potential ka relation: E = −dV/dr. Uniform field ke case mein: E = −ΔV/Δr.

Q4. Kya E = 0 ka matlab V = 0 hota hai?

Nahi. E = 0 ka matlab potential constant hai. Constant potential zero bhi ho sakta hai aur non-zero bhi.

Q5. Equipotential surface par work done zero kyun hota hai?

Equipotential surface par potential difference zero hota hai: ΔV = 0. Therefore: W = qΔV = 0.

Q6. Electric field kis direction mein point karta hai?

Electric field higher potential se lower potential ki direction mein point karta hai.

Q7. Do charges ki potential energy ka formula kya hai?

Two charges q₁ and q₂ separated by r: U = kq₁q₂/r.

Q8. Conductor ke inside potential kya hota hai?

Electrostatic equilibrium mein conductor ke inside electric field zero hota hai aur potential constant hota hai.

Q9. Multiple charges ke potential ko kaise calculate karte hain?

Har charge ka individual potential calculate karke algebraically add karo: V_net = ΣV.

Q10. Infinite line charge ke liye reference distance kyun chahiye?

Infinite line charge ke case mein potential ko infinity par zero reference nahi kiya ja sakta. Isliye ek finite reference distance r₀ choose ki jaati hai.

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Final Thoughts

Electric Potential ko strong karne ke liye sabse pehle iska scalar nature samjho. Ye ek aisa concept hai jo electric field, work aur potential energy ko ek common framework mein connect karta hai.

JEE Main ke questions mein sabse frequently useful formulas hain: V = kQ/r, V_net = ΣV, U = qV aur E = −dV/dr.

Saath hi teen concepts ko kabhi confuse mat karna: potential scalar hai, electric field vector hai, aur E = 0 ka matlab V = 0 nahi balki V constant hai.

Agar aap point charge, multiple charges, potential energy aur equipotential surface ke concepts ko logically connect kar lete ho, toh Electric Potential ke numerical aur conceptual questions dono significantly easier ho jaate hain.