Maths and Physics Tuition/Tests/Notes

Energy in a Uniform Electric Field

When an electric charge is placed in an electric field, it experiences a force. This means that if it moves from one point to another, in general, electric potential energy will be lost or gained: work will be done. If the charge moves in the direction...

Gravitational Potential

We can define a quantity that gives a measure of the amount of energy a body of unit mass has when in a gravitational field. This quantity is called the gravitational potential and is defined as where is the work that must be done to remove a body to a...

The Gravitational Redshift

One of the predictions of general relativity is that clocks in the region of a gravitational field run slowly. A clock on the ground floor of a building will run more slowly than a clock at the top. Equivalently, light moving away from a mass undergoes...

Damped and Forced Vibrations

Free undamped, unforced vibrations in simple harmonic motion obey the equation or Typically the vibration will be subject to a resistive term R, which for low speeds is proportional to velocity and in the opposite direction hence The equation for...

Energy in Electric Fields in the Presence of Dielectrics

We can illustrate how energy is stored in an electric field using the example of a parallel plate capacitor. The capacitor is initially uncharged, and a potential difference is built up between the plates by transferring a charge from one plate to the...

Fermat's Principle

Fermat's principle states that the path taken between two points by a ray of light is the path that can be traversed in the least time and can be taken to define the path taken by a light ray. Equivalently we may say that the optical path length is the...

Proof of Thin Lens Equation

The thin lens equation – – where is the focal length is the distance of the object from the lens is the distance of the image from the lens can be easily derived using properties of similar triangles. The triangles CAB and CDE are similar, so (1)where...

Kernels and Images of Homomorphisms

Given two groups and a group homomorphism from to is a function such that for all where the group operation on the left hand side of the equation is that of and on the right hand side that of maps the identity element of G to the identity element of...

Parametric Equations

We can define a curve \[y=f(x)\] para metrically by introducing a convenient parameter which defines a point on a curve. The parameter may define for example the length along the curve from a given point, and this is useful for some purposes. Example:...

Volume of a Sphere

In spherical polar coordinates a volume element is \[dV=r^2sin \theta d \phi d \theta dr\] where \[0 \le 0 \phi \lt 2 \pi\] is the anticlockwise angle from the positive \[x\] axis to a line drawn from the origin to the projection of a point onto the...

O Level Additional Maths Notes

A Level Physics Notes - Medical Physics

Humidity Requirements

Relative humidity is often an important factor in industry. During the manufacture of cotton cloth, the cotton fibres must not be allowed to become too dry, or they willbecome brittle and easily accumulate static electricity, which causes its own...

Lost Volts

The emf of a cell may be measure accurately by connecting it directly to a high resistance voltmeter. (below right). Let us suppose that a voltmeter connected to the terminals battery of internal resistance gives a reading of gives a reading of This is...

Relative Humidity

Persperation – the evaporation of moisture from the skin – is an important factor in controlling body temperature. The rate at which evaporation takes place depends on three factors: the temperature the amount of water vapour present in the air the...

Spherical Mirrors of Large Aperture

The thin lens equation where is the focal length is the object distance is the image distance only applies to spherical mirrors (or thin lenses) of small aperture. If the mirror has a large aperture, a sharp image is not formed. If a hemispherical...

The Steelyard

The steelyard is a balance used for measuring weights. It has been used since Roman times, and is especially useful where portability is required, or where the weight to be measured can be suspended from a hook – bags of gold or rice for example. The...

Young's Double Slit Experiment

This experiment was very important in demonstrating the wave nature of light. It is very simple, consisting only of a light source and two screens, one with two slits. Light passes through each slit, and the light that passes through each slit...

Refraction and Spectra

You have probably seen how white light produces a spectrum when it passes through a glass block: This is due to the phenomenon of refraction. When waves pass from one medium to another, the direction and speed of the waves may change. The change may...

Specific and Latent Heat

In general a substance may exist in more than one form – solid, liquid or gas.. To turn a substance from a solid to a liquid of a liquid to a gas needs energy. To heat a solid, liquid or gas also needs energy. To heat m Kg ice by T degrees Celsius (or...