Physics Tutor in MIHAN Nagpur – Electric Field Intensity on Axial Point Due to Uniformly Charged Ring
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Electric Field Intensity at Axial Point Due to a Uniformly Charged Ring
Consider a uniformly charged ring of radius R. Total charge on the ring is Q. We have to find electric field intensity at a point P on the axis of the ring. The distance of point P from the centre O of the ring is x.
Diagram
P
|
| x
|
O
/ \
/ \
| Ring |
\ /
\_____/
Radius of ring = R
Total charge = Q
Point P is on the axis of the ring
Take a small charge element dq on the ring.
Distance of dq from point P is:
r = sqrt(R^2 + x^2)
Electric field due to dq at point P is:
dE = (1 / 4πε0) * dq / r^2
Now,
r^2 = R^2 + x^2
So,
dE = (1 / 4πε0) * dq / (R^2 + x^2)
The electric field dE can be resolved into two components:
Axial component
Perpendicular component
Due to symmetry, perpendicular components cancel each other. Only axial components add.
Axial component:
dE cosθ
From the diagram,
cosθ = x / sqrt(R^2 + x^2)
Therefore,
dE_axial = dE cosθ
dE_axial = (1 / 4πε0) * dq / (R^2 + x^2) * x / sqrt(R^2 + x^2)
dE_axial = (1 / 4πε0) * x dq / (R^2 + x^2)^(3/2)
Now integrate over the complete ring:
E = ∫ dE_axial
E = (1 / 4πε0) * x / (R^2 + x^2)^(3/2) ∫ dq
Since,
∫ dq = Q
Therefore,
E = (1 / 4πε0) * Qx / (R^2 + x^2)^(3/2)
This is the electric field intensity at an axial point due to a uniformly charged ring.
Final Formula
E = (1 / 4πε0) * Qx / (R^2 + x^2)^(3/2)
Where:
E = electric field intensity at axial point
Q = total charge on ring
R = radius of ring
x = distance of point from centre
ε0 = permittivity of free space
Special Cases
Case 1: At the centre of the ring
At centre,
x = 0
So,
E = 0
Therefore, electric field at the centre of a uniformly charged ring is zero.
Case 2: When x is very large
If x >> R, then:
R^2 + x^2 ≈ x^2
So,
E = (1 / 4πε0) * Q / x^2
This means that from a very large distance, the charged ring behaves like a point charge.
Kumar Sir Style Explanation
Kumar Sir explains this concept in a very simple way. First, understand that every small charge element dq produces electric field at point P. But because the ring is symmetric, the side components cancel. Only the components along the axis survive. That is why we multiply by cosθ and integrate over the complete ring.
This is the most important concept in this derivation. Once symmetry is clear, the derivation becomes very easy.
Why Students in MIHAN Nagpur Need Strong Physics Concepts
Many students learn formulas but get confused in derivations. In NEET, JEE and CBSE exams, questions are often based on concept clarity. If you understand why perpendicular components cancel and why axial components add, then you can solve many electrostatics questions easily.
Kumar Sir focuses on:
Concept clarity
Step-by-step derivation
Numerical practice
NEET and JEE level questions
CBSE board explanation
AP Physics and IB Physics approach
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Properties of Electric Field Lines
Electric field lines start from positive charge and end on negative charge.
The tangent at any point on an electric field line gives the direction of electric field at that point.
Electric field lines never intersect each other.
Electric field lines are closer where electric field is strong.
Electric field lines are farther apart where electric field is weak.
In a uniform electric field, field lines are straight, parallel and equally spaced.
Electric field lines are perpendicular to the surface of a conductor.
Inside a conductor in electrostatic condition, electric field is zero.
Electric field lines do not form closed loops.
The number of field lines is proportional to the magnitude of charge.
Why Electric Field Lines Never Intersect
Electric field lines never intersect because at any point, electric field has only one definite direction. If two field lines intersect, then at the point of intersection there will be two tangents, meaning two directions of electric field at the same point. This is physically impossible. Therefore, electric field lines cannot intersect.
15 Conceptual Questions with Answers
1. What are electric field lines?
Electric field lines are imaginary lines used to represent the direction and strength of an electric field.
2. From where do electric field lines start?
They start from positive charge.
3. Where do electric field lines end?
They end on negative charge.
4. What does the tangent to an electric field line represent?
It represents the direction of electric field at that point.
5. Can electric field lines intersect?
No, electric field lines never intersect.
6. Why do electric field lines not intersect?
Because electric field cannot have two directions at the same point.
7. What does closer spacing of field lines show?
It shows a stronger electric field.
8. What does larger spacing between field lines show?
It shows a weaker electric field.
9. How are field lines in a uniform electric field?
They are straight, parallel and equally spaced.
10. Are electric field lines closed loops?
No, electric field lines do not form closed loops.
11. What is the direction of field lines near a positive charge?
They are directed away from the positive charge.
12. What is the direction of field lines near a negative charge?
They are directed towards the negative charge.
13. What is electric field inside a conductor in electrostatic condition?
Electric field inside a conductor is zero.
14. How do field lines meet the surface of a conductor?
They meet the conductor surface normally, or perpendicular to the surface.
15. What does the number of field lines represent?
The number of field lines represents the magnitude of charge or strength of electric field.