Physics Tutor in Wardha Road Nagpur – Spherical Capacitor and Cylindrical Capacitor Derivation 

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If you are searching for Physics Tutor in Wardha Road Nagpur, then Kumar Sir’s one-to-one Physics classes can help you understand difficult Class 12, NEET and JEE topics like spherical capacitor, cylindrical capacitor, concentric spherical capacitor, electric field, potential difference and capacitance with full concept clarity.

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1. Basic Formula of Capacitance

Capacitance is the ability of a conductor system to store charge.

Copy-paste friendly formula:

C = Q / V

Where:

C = capacitance
Q = charge stored
V = potential difference

For derivation, we generally follow this method:

1. Give charge +Q to inner conductor.

2. Give charge -Q to outer conductor.

3. Find electric field using Gauss law.

4. Find potential difference.

5. Use C = Q / V.

2. Spherical Capacitor Derivation

A spherical capacitor consists of two concentric spherical conducting shells. Let the radius of inner sphere be a and radius of outer sphere be b.

Diagram idea for website:

Inner sphere radius = a
Outer sphere radius = b
Charge on inner sphere = +Q
Charge on outer sphere = -Q

Electric field between the two spheres at distance r from centre is:

E = Q / (4πε0 r²)

Potential difference between inner and outer sphere:

V = ∫ from a to b E dr

So:

V = ∫ from a to b [Q / (4πε0 r²)] dr

V = Q / (4πε0) ∫ from a to b r⁻² dr

V = Q / (4πε0) [ -1/r ] from a to b

V = Q / (4πε0) [ 1/a – 1/b ]

Now capacitance:

C = Q / V

C = Q / { Q / (4πε0) [ 1/a – 1/b ] }

C = 4πε0 / [ 1/a – 1/b ]

C = 4πε0 ab / (b – a)

Final formula:

C = 4πε0 ab / (b – a)

If dielectric medium of dielectric constant K is present:

C = 4πε0 K ab / (b – a)

3. Isolated Spherical Conductor Capacitance

If outer sphere is at infinity, then:

b = infinity

For spherical capacitor formula:

C = 4πε0 ab / (b – a)

When b → infinity, capacitance becomes:

C = 4πε0 a

Final formula:

C = 4πε0 R

Where R is radius of isolated spherical conductor.

This is very important for NEET and JEE.

4. Concentric Spherical Capacitor

Concentric spherical capacitor means both spherical shells have same centre.

Let:

Inner radius = R1
Outer radius = R2
Charge = Q

Electric field exists only between R1 and R2.

Electric field:

E = Q / (4πε0 r²)

Potential difference:

V = Q / (4πε0) [ 1/R1 – 1/R2 ]

Capacitance:

C = Q / V

Final formula:

C = 4πε0 R1 R2 / (R2 – R1)

With dielectric:

C = 4πε0 K R1 R2 / (R2 – R1)

Important concept:

If distance between shells is small, capacitance becomes large.

5. Cylindrical Capacitor Derivation

A cylindrical capacitor consists of two coaxial cylinders.

Let:

Radius of inner cylinder = a
Radius of outer cylinder = b
Length of cylinder = L
Charge per unit length = λ
Total charge = Q = λL

Using Gauss law, electric field at distance r from axis is:

E = λ / (2πε0 r)

Potential difference between inner and outer cylinder:

V = ∫ from a to b E dr

V = ∫ from a to b [λ / (2πε0 r)] dr

V = λ / (2πε0) ∫ from a to b dr/r

V = λ / (2πε0) ln(b/a)

Now capacitance per unit length:

C/L = λ / V

C/L = 2πε0 / ln(b/a)

Total capacitance:

C = 2πε0 L / ln(b/a)

With dielectric:

C = 2πε0 K L / ln(b/a)

Final formula:

C = 2πε0 L / ln(b/a)

6. Important Comparison Table

Kumar Sir Style Concept Building

Kumar Sir teaches these derivations step by step. First, he explains the physical structure of capacitor. Then he explains where electric field exists and where it becomes zero. After that, he uses Gauss law and potential difference to reach the capacitance formula.

Many students directly memorize:

C = 4πε0 ab / (b – a)

or

C = 2πε0 L / ln(b/a)

But Kumar Sir teaches why these formulas come. This helps students solve modified questions in NEET, JEE Main, JEE Advanced, CBSE, IB and AP Physics.

Why Students on Wardha Road Nagpur Should Learn from Kumar Sir

If you live near Wardha Road Nagpur and Physics is difficult for you, especially electrostatics, capacitors, Gauss law, potential, electric field and derivations, then you should contact Kumar Sir.

Kumar Sir has 30 years teaching experience and teaches Physics one-to-one online. He focuses on:

• Concept clarity

• Derivation understanding

• Numerical practice

• Doubt solving

• NEET and JEE previous year questions

• CBSE board derivations

• IB, AP, IGCSE and A-Level Physics support

For serious Physics preparation, choose Kumar Sir.

Call / WhatsApp: +91-9958461445
Website: Kumar Physics Classes

Applications of Spherical, Cylindrical and Concentric Spherical Capacitors

Spherical capacitor and concentric spherical capacitor are mainly used where charge distribution, high voltage insulation and electric field control are important. In practical devices, exact spherical capacitors are not very common in mobile phones and laptops, but their concept is used in sensors, high-voltage equipment, electrostatic shielding, surge protection and calibration instruments.

A concentric spherical capacitor is useful in high-voltage laboratories because its electric field is symmetrical and easy to calculate. It is used for studying insulation strength, dielectric testing, charge storage experiments and electrostatic field measurement.

Cylindrical capacitors are more common in practical industry because many cables and electronic components have cylindrical geometry. A coaxial cable behaves like a cylindrical capacitor because it has an inner conductor, outer conductor and dielectric between them.

Applications of cylindrical capacitor concept:

• Coaxial cables

• RF communication lines

• Antenna systems

• Cable TV lines

• Internet broadband cables

• High-frequency signal transmission

• Shielded wires

• Power cables

In mobile phones, capacitors are used for filtering, signal coupling, decoupling, noise reduction, RF tuning and power management. The capacitor may not look like a big spherical or cylindrical capacitor, but the same capacitance concepts are used in tiny ceramic capacitors and RF circuits.

In laptops, capacitors are used in motherboard power supply circuits, charging circuits, display circuits, processor voltage regulation, audio circuits, Wi-Fi circuits and battery management systems.

In grid lines and power systems, capacitor banks are used for power factor correction, voltage regulation and reducing power loss. Cylindrical capacitor concepts are also seen in high-voltage cables, where the conductor and outer shield form a cylindrical capacitor.

In transmission lines, capacitance exists naturally between conductors and between conductor and earth. This affects charging current, voltage stability and power transmission efficiency.

So, in simple words:

Spherical capacitor concept is useful in high-voltage electrostatics and field measurement.

Concentric spherical capacitor concept is useful in controlled electric field experiments and insulation testing.

Cylindrical capacitor concept is widely used in cables, communication lines, RF systems and power transmission.

नीचे copy-paste friendly format में लिख दीजिए:

Capacitor Numerical – Kumar Sir Style

Question:
A capacitor of capacitance 2 μF is connected across a battery of 12 V. Find the charge stored on the capacitor and energy stored in the capacitor.

Given Data

Capacitance:

C = 2 μF

C = 2 × 10⁻⁶ F

Potential difference:

V = 12 V

Formula for Charge

Q = C V

Now put the values:

Q = 2 × 10⁻⁶ × 12

Q = 24 × 10⁻⁶ C

Q = 24 μC

So, charge stored on the capacitor is:

Q = 24 μC

Formula for Energy Stored

U = 1/2 C V²

Now put the values:

U = 1/2 × 2 × 10⁻⁶ × 12²

U = 1 × 10⁻⁶ × 144

U = 144 × 10⁻⁶ J

U = 144 μJ

So, energy stored in the capacitor is:

U = 144 μJ

Final Answer

Charge stored = 24 μC

Energy stored = 144 μJ

Kumar Sir Concept

Capacitor का काम charge और energy store करना होता है। अगर capacitance और voltage दिए हों, तो पहले हमेशा charge निकालो:

Q = C V

और energy के लिए use करो:

U = 1/2 C V²

NEET और JEE में capacitor के questions में unit conversion बहुत important होता है। हमेशा याद रखो:

1 μF = 10⁻⁶ F