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Electric Potential of Uniformly Charged Ring, Rod, and Disc
Electric Potential Due to a Charged Ring
Let electric potential at point P due to small element of length dℓ be dV.
(distance between small element and point P is equal to r)
Electric potential due to whole ring
Potential Due to a Uniformly Charged Rod
Electric Potential due to a uniformly charged rod of length L and linear charge density lambda, at a point P on its axial line which is d units away from it
Charge per unit length λ = Q/L
Charge of slice dq = λ.dx
Electric potential: 
Potential Due to a Uniformly Charged Disc
Find the electric potential at the axis of a uniformly charged disc and use potential to find the electric field at same point.
Potential due to ring element of radius r and thickness dr is dv:
The document Electric Potential of Uniformly Charged Ring, Rod, and Disc is a part of the JEE Course Additional Study Material for JEE.
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FAQs on Electric Potential of Uniformly Charged Ring, Rod, and Disc
| 1. How do I find the electric potential at the center of a uniformly charged ring? |  |
Ans. The electric potential at the center of a uniformly charged ring equals kQ/R, where k is Coulomb's constant, Q is total charge, and R is the ring's radius. Since all charge elements are equidistant from the center, distances don't vary-only the arithmetic sum matters, not vector addition like with electric field. This makes ring problems simpler than disc or rod calculations.
| 2. What's the difference between electric potential of a charged ring versus a charged disc? | |
Ans. A uniformly charged ring produces uniform potential along its axis because charge elements maintain equal distances from any axial point. A uniformly charged disc's potential varies non-uniformly along the axis since charge distribution changes with position. Ring potential follows simpler algebraic relationships; disc potential requires integration over radial elements and yields more complex expressions involving square roots.
| 3. Why is the electric potential formula different for a rod compared to a ring? | |
Ans. A rod's charge distributes linearly along one dimension, requiring integration using linear charge density (λ). Ring charge distributes around a circle maintaining constant radius, allowing direct summation. Rod potential depends on distance measurements from the rod's endpoints; ring potential depends only on axial distance. These geometric differences produce fundamentally different mathematical expressions and solution methods.
| 4. Can I use the same approach to calculate electric potential for both finite and infinite uniformly charged rods? | |
Ans. No-finite rod calculations use integration with logarithmic expressions involving endpoint distances, while infinite rod potential approaches infinity (requiring reference point adjustments). Finite rods allow direct potential comparisons; infinite rods require differential potential calculations. For JEE problems, finite rods are standard; infinite cases appear in theoretical discussions only.
| 5. How does the position on the axis affect electric potential of a uniformly charged disc? | |
Ans. Electric potential of a uniformly charged disc along its axis depends on axial distance and follows the expression σ(√(R²+z²)-z)/(2ε₀), where z is distance from the disc's center and R is its radius. As z increases, potential decreases. At the disc's surface (z=0), potential is maximum; at infinity, it approaches zero, following characteristic decay patterns.
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