SOME IMPORTANT LAWS

PRERNA FOR IAS

SOME IMPORTANT LAWS

1. Biot–Savart Law

Biot–Savart Law gives the magnetic field produced by a small current element. It states that the magnetic field depends on current, distance, and the angle between the current element and the observation point. This law is fundamental for calculating magnetic fields around wires, loops, coils, and current-carrying conductors.

2. Ampere’s Circuital Law

Ampere’s Circuital Law states that the line integral of magnetic field around a closed path equals μ₀ times the enclosed current. It is useful for calculating magnetic fields in symmetrical situations such as straight conductors, solenoids, and toroids. The law simplifies magnetic field calculations significantly.

3. Motion of Charge Particle in Uniform Magnetic Field

A charged particle moving in a uniform magnetic field experiences a magnetic force perpendicular to its velocity. This force changes only the direction, not the speed, of the particle. The particle follows a circular path with radius depending on mass, charge, velocity, and magnetic field strength.

4. Motion of Charge Particle in Uniform Electric Field

A charged particle in a uniform electric field experiences a constant force equal to qE. This force produces constant acceleration, causing the particle’s velocity to change with time. Its motion is similar to uniformly accelerated motion in mechanics and is important in particle accelerators and cathode-ray devices.

5. Cyclotron

A cyclotron is a device used to accelerate charged particles to high speeds using electric and magnetic fields. The particle moves in a spiral path while gaining energy. Cyclotrons are used in nuclear physics, medical isotope production, and scientific research. Their frequency depends on charge, mass, and magnetic field.

6. Force Between Two Parallel Current-Carrying Conductors

Two parallel conductors carrying current exert magnetic forces on each other. Currents flowing in the same direction attract, while currents in opposite directions repel. The force depends on the currents, length of conductors, and distance between them. This principle helps define the SI unit of current, ampere.

7. Torque on a Current Loop