Electromagnetism: Laws, Concepts, and Applications
Fundamental Laws of Electromagnetism
1. Coulomb’s Law
It states that the force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
2. Gauss’s Law
It states that the total electric flux through a closed surface is equal to times the net charge enclosed within the surface.
3. Biot-Savart Law
It states that the magnetic field due to a small element of current at a point in space is directly proportional to the current, the length of the element, and the sine of the angle between the current element and the line joining the element to the point, and inversely proportional to the square of the distance.
4. Ampere’s Law
It states that the line integral of the magnetic field around a closed loop is proportional to the total current enclosed by the loop.
5. Kirchhoff’s Laws
Kirchhoff’s Current Law
The sum of currents entering a junction is equal to the sum of currents leaving the junction.
Kirchhoff’s Voltage Law
The sum of the electromotive forces (emf) and potential differences in any closed loop of a circuit is zero.
Electrostatic Potential and Equipotential Surfaces
Electrostatic Potential
It is the work done to bring a unit positive charge to a point against the electric force of the field.
Equipotential Surface
It is a surface having the same electrostatic potential at all points.
Properties of Equipotential Surfaces
- The electric field will always be normal to the equipotential surface.
- The work done to move a charge along an equipotential surface is zero (W = 0).
Reasons for these Properties
- If the electric field has a component parallel to the equipotential surface, electrons will drift according to the field, and you will get current at stationary conditions, which is not possible.
- V = W/q, W = V.q. In an equipotential surface, all the points have the same potential. There is no potential difference.
Dielectrics
There are some materials that do not conduct electricity but still transmit electrical effects. These substances are called dielectrics.
Polar and Non-Polar Dielectrics
If the centers of gravity of the positive nuclei and the electron cloud coincide, the molecule is called a non-polar molecule. Its dipole moment is zero. If the centers of gravity of the positive nuclei and the electron cloud do not coincide, the molecule is called a polar molecule.
Electric Polarization
When a non-polar atom is placed in an electric field, the positively charged nucleus is pulled along the direction of the electric field, and electrons are pulled in the opposite direction. Finally, the centers of positive charges and negative charges are separated by a distance, and the atom gets an induced dipole moment. This is called electric polarization.
EMF and Ohm’s Law
Electromotive Force (EMF)
EMF, or electromotive force, refers to the energy provided by a source such as a battery or generator per unit charge to move electric charges through a circuit.
Ohm’s Law
Ohm’s Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.
Temperature Coefficient of Resistance
The temperature coefficient is defined as the ratio of the increase in resistance for a unit degree rise of temperature to resistance at 0°C.
- Positive Temperature Coefficient of Resistance: Metals have a positive temperature coefficient. Hence resistance increases with a rise in temperature.
- Negative Temperature Coefficient of Resistance: Insulators and semiconductors have a negative temperature coefficient of resistance. Resistance decreases with an increase in temperature.
- Zero Temperature Coefficient of Resistance: Certain alloys like manganin, constantan, etc., have a zero temperature coefficient. Hence the resistance of these substances does not vary with temperature. These alloys are used for making standard resistance coils.
Galvanometer
A moving coil galvanometer is an instrument used to detect and measure small electric currents. It works on the principle that a current-carrying conductor placed in a magnetic field experiences a torque.
Working of a Galvanometer
- A rectangular coil, wound on a metallic frame, is placed between the poles of a permanent magnet. The coil is suspended by a spring, and a pointer is attached to it.
- When an electric current passes through the coil, it experiences a magnetic force due to the magnetic field, causing it to rotate.
- The rotation of the coil moves the pointer over a scale. The angle of deflection of the pointer is proportional to the current flowing through the coil.
- The restoring torque produced by the spring balances the magnetic torque, allowing the pointer to settle at a position corresponding to the current.
Conversion of a Galvanometer
1. Galvanometer to Ammeter
To convert a galvanometer into an ammeter, a low resistance, known as a shunt, is connected in parallel with the galvanometer. This allows most of the current to bypass the galvanometer, enabling it to measure higher currents without being damaged.
2. Galvanometer to Voltmeter
To convert a galvanometer into a voltmeter, a high resistance is connected in series with the galvanometer. This allows the device to measure higher voltages by limiting the current that passes through it.