Van de Graaff Generators, Electric Current, and Ohm's Law

Van de Graaff Generator Principles

The Van de Graaff generator is a machine capable of building high voltages on the order of millions of volts. These large electric fields are utilized to accelerate charged particles—such as electrons, protons, and ions—to the high energies required for experiments probing the small-scale structure of matter.

Operating Principle

Consider a large spherical conducting shell of radius R carrying a charge Q. This charge distributes itself uniformly across the sphere:

• Field outside: Equivalent to a point charge Q at the center.
• Field inside: Vanishes completely.
• Potential: Constant inside the sphere, equal to the value at radius R.

Understanding Electric Current

To define electric current, imagine a small area held normal to the direction of charge flow. If q+ is the net positive charge and q– is the net negative charge flowing forward in time t, the net charge q is calculated as:

q = q+ – q–

For steady current, this flow is directly proportional to the time interval t.

Ohm's Law Explained

Discovered by G.S. Ohm in 1828, Ohm's Law describes the relationship between current and potential difference in a conductor. For a conductor with current I and potential difference V, the law states:

V ∝ I or V = RI

Limitations of Ohm's Law

While valid for many materials, some devices exhibit deviations from this proportionality:

• Non-linearity: V ceases to be proportional to I.
• Directional dependence: The relationship between V and I depends on the sign of V; reversing the voltage does not produce a current of the same magnitude.