Van de Graaff Generator

Q: Is this compatible with MathJax?

Yes. All LaTeX expressions in this file work perfectly with MathJax.

Q: Can I use this in WordPress?

Yes. Paste this code inside a Custom HTML block.

Q: Is JavaScript required?

No. Everything works using only HTML and CSS.

Q: Is this SEO-friendly?

Yes. Semantic tags, headings, and structured content help SEO.

Van de Graaff Generator

Published: December 15, 2025 •

Van de Graaff Generator

Van de Graaff Generator

The Van de Graaff Generator is a device used to generate very high electric potentials of the order of $10^7$ volts. These high potentials are used to accelerate charged particles to very high energies for nuclear physics experiments.

Question 1: What is a Van de Graaff Generator?

Answer:

It is a device used to produce very high electrostatic potentials.
The potential developed is of the order of $10^7$ volts.
The high electric field is used to accelerate charged particles such as:
- Electrons
- Protons
- Ions
It is mainly used in nuclear physics experiments.
It was designed by Van de Graaff in the year 1931.

Question 2: State the principle of Van de Graaff Generator.

Answer:

The working of a Van de Graaff generator is based on the following principles:

Corona discharge: Charge is emitted easily from sharp pointed conductors.
Charge distribution on hollow conductors: When charge is given to a hollow conductor, it is transferred to its outer surface and distributes uniformly.
Continuous charging: If charge is continuously supplied to an insulated conductor, its potential keeps on increasing.

Question 3: Describe the construction of a Van de Graaff Generator.

Answer:

An endless insulating belt made of rubber or silk moves over two pulleys P₁ and P₂.
The lower pulley P₁ is driven by an electric motor.
A spray brush A with sharp points is connected to a high-voltage DC supply.
The spray brush deposits positive charge on the moving belt.
A collector brush C collects the charge from the belt.
The collector brush is connected to a large hollow metallic dome D.
The dome is mounted on insulating pillars.
An evacuated accelerating tube E has an electrode I connected to the dome.
The entire system is enclosed in a steel vessel filled with nitrogen and a small amount of Freon gas.
The vessel is earthed to prevent charge leakage.

Question 4: Explain the working of a Van de Graaff Generator.

Answer:

The motor rotates the lower pulley, setting the belt into motion.
The DC power supply is switched on.
Positive charge is sprayed onto the belt from the sharp points of brush A.
The moving belt carries the positive charge upward.
The charge is collected by brush C.
The collected charge is transferred to the hollow metallic dome.
The charge spreads uniformly over the outer surface of the dome.
Continuous charging raises the potential of the dome to a very high value.
The electrode connected to the dome also attains the same high potential.
Positive ions (protons or deuterons) introduced in the accelerator tube are repelled.
These ions accelerate downward due to the large potential difference.
The accelerated particles acquire very high kinetic energy.
They are directed to strike a target for nuclear experiments.

Question 5(a): What is the energy of particles produced by a Van de Graaff Generator?

Answer:

The charged particles acquire energies of the order of $10\,\text{MeV}$ .
This high energy is suitable for nuclear reactions and research.

Question 5(b): How emf is generated in a Van de Graaff Generator?

Answer:

In a Van de Graaff Generator the electrons are literally loaded into a conveyor belt and swept along to create a potential difference.
A generator utilises the movement of wire through a magnetic field to produce motional emf/current through a circuit.

Question 6: State the uses of a Van de Graaff Generator.

Answer:

To cause disintegration of atomic nuclei.
To produce radioactive isotopes.
To study nuclear structure.
To study different types of nuclear reactions.
To accelerate electrons for:
- Food sterilization
- Material processing

Question 7 (MCQ): The Van de Graaff generator works on the principle of

(a) Electromagnetic induction
(b) Thermionic emission
(c) Corona discharge and charge accumulation
(d) Photoelectric effect

Answer:

(c) Corona discharge and charge accumulation

Explanation:

Sharp points produce corona discharge and continuous supply of charge to an insulated conductor increases its potential.

Question 8 (MCQ): The belt in a Van de Graaff generator is made of

(a) Copper
(b) Iron
(c) Insulating material
(d) Semiconductor

Answer:

(c) Insulating material

Explanation:

An insulating belt prevents charge leakage and efficiently transports charge to the dome.

Question 9 (MCQ): The maximum potential developed by a Van de Graaff generator is of the order of

(a) $10^3$ V
(b) $10^5$ V
(c) $10^7$ V
(d) $10^9$ V

Answer:

(c) $10^7$ V

Explanation:

Van de Graaff generators are designed to produce extremely high voltages of the order of ten million volts.

Question 10 (MCQ): The function of nitrogen and Freon gas inside the vessel is to

(a) Cool the belt
(b) Increase ion production
(c) Improve insulation and prevent charge leakage
(d) Reduce friction

Answer:

(c) Improve insulation and prevent charge leakage

Explanation:

High-pressure nitrogen mixed with Freon increases dielectric strength and prevents electrical discharge.

✦✦✦ End of Solution ✦✦✦

Key Takeaways:

Always use curly braces {} around numerator and denominator in fractions
\frac{a}{b} is preferred over a \div b for professional mathematical typesetting
Use \boxed{} to emphasize important formulas in your document
For inline fractions in text, consider using / or \nicefrac{}{} for better readability

Frequently Asked Questions (FAQ)

Is this compatible with MathJax?

Yes, absolutely! All LaTeX expressions shown in this tutorial work perfectly with MathJax, which is the most popular JavaScript library for displaying mathematical notation in web browsers. You can use these commands in any website that supports MathJax rendering.

Can I use this in WordPress?

Yes, you can use these LaTeX commands in WordPress. Simply paste the code inside a Custom HTML block, or use a LaTeX plugin like WP QuickLaTeX or MathJax-LaTeX. Many WordPress themes also have built-in LaTeX support for mathematical content.

Is JavaScript required for this page?

No, JavaScript is not required. This entire page works using only HTML5 and CSS3, making it lightweight, fast-loading, and accessible. The FAQ accordion functionality uses native HTML5 elements.

Is this SEO-friendly?

Yes, this page is highly SEO-friendly. It uses semantic HTML5 tags, proper heading hierarchy (H1, H2), structured data (Schema.org markup), meta descriptions, Open Graph tags, and mobile-responsive design. All of these factors help search engines understand and rank your content better.

What's the difference between \frac and \div?

The \frac{a}{b} command creates a vertical fraction (a over b), which is the standard mathematical notation. The \div command creates the division symbol (÷), which is less commonly used in professional mathematics. In academic and professional contexts, \frac is strongly preferred.

How do I make fractions display better in inline text?

For inline fractions within paragraphs, you can use \tfrac{a}{b} for a smaller "text-style" fraction, or use the forward slash like a/b. Some packages also provide \nicefrac{a}{b} which creates diagonal fractions that blend better with surrounding text.

Download Materials

Comments (0)