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Introduction
The branch of physics which deals with magnetism due to the electric current is called electromagnetism. For a long time it was hard to believe if there existed a relation between electricity and magnetism.
Biot and Savart's Law
The Biot - Savart's law enables us to write the general results for the magnetic field due to an arbitrary current distribution or it is an experimental law predicted by Biot and Savart dealing with magnetic field strength at a point due to a small current element.
Evaluation of Magnetic Field
Consider a straight conductor XY carrying a current I as shown. To find the magnetic field at P, consider a small current element of length dl.
Ampere's Circuital Law
Ampere's law is a useful relation that is analogous to Gauss's law. Ampere's law is a relationship between the tangential component of magnetic field at points on a closed curve and the net current through the area bounded by the curve.
The Solenoid and the Toroid
Toroid is a hollow circular ring (like a medu vadai) on which a large number of turns of a wire are wound.
Lorentz Force
The force experienced by a charged particle moving in space where both electric and magnetic field exist is called lorentz force.
Cyclotron
The sub-atomic charged particles experience large forces when subjected to electric and magnetic fields due to their extremely small mass. In nuclear physics such energized particles are used to bombard nuclei causing nuclear reactions. This helps to obtain information about the nucleus.
The Ampere
Force between Two Parallel Conductors Carrying Currents
The Current Loop as a Magnetic Dipole
When an electric current flows in a closed loop of wire, placed in a uniform magnetic field, the magnetic forces produce a torque which tends to rotate the loop so that area of the loop is perpendicular to the direction of the magnetic field.
Moving Coil Galvanometer
A moving coil galvanometer is an instrument used for detection and measurement of small electric currents.
Summary
The Biot-Savart law asserts that the magnetic field dB due to an element dl carrying a steady current i at a point P at a distance r from the current element.
Numerical 01
The magnetic field at the centre of a circular current carrying coil.
Numerical 02
Two wires A and B have the same length of 44 cm, and carry a current of 10 A each. Wire A is bent into a circle and wire B is bent into a square. (a) Which wire produces a greater magnetic field at the centre? (b) Obtain the magnitudes of the fields at the centres of the two wires.
Numerical 03
Two concentric circular coils X and Y of radii 16cm and 10cm respectively lie in the same vertical plane containing the north-south direction.
Numerical 04
A solenoid 50cm long has 4 layers of windings of 350 turns each. The radius of the lowest layer is 1.4cm.
Numerical 05
A long straight wire carries a current of 4A. What is the magnetic field at a point distant 10cm from the wire?
Numerical 06
Two concentric circles of radius 2 cm and 4 cm respectively carry currents of 2A and 4A in a clockwise direction.
Numerical 07
A given length L of a uniform wire is bent (i) into a single circular turn and (ii) into n identical circular turns. What is the ratio of the magnetic field at the center of the coil in both the cases mentioned above when same current is passed through them?
Numerical 08
In the Bohr model of the hydrogen atom the electron revolves around the nucleus in a path of radius 5.1 x 10-11 m at a frequency of 6.8 x 1015 revolution per second.
Numerical 09
A long, thin straight solenoid has 500 turns wound over a length of 50cm. It carries a current of 0.5A. What is the magnetic field inside this solenoid?
Numerical 10
A straight solenoid has 400 turns wound on a cylinder of radius 5cm and length 40cm. What is the magnetic field at the mid-point of solenoid when a current of 2A flows in it?
Numerical 11
Two solenoids P and Q have length and the total number of turns in the ratio of 1:2. What is the ratio of the magnetic field inside the two solenoids due to the same current?
Numerical 12
An electron is projected with a speed of 105ms-1 at right angles to a magnetic field of 0.019 G. Calculate the radius of the circle described by the electron.
Numerical 13
An electron is accelerated from rest through a potential difference of 3 KV. It enters into the region of a uniform, perpendicular magnetic field of 0.2T. What is the radius of the path of electron inside the field?
Numerical 14
A straight horizontal conducting rod of length 0.45 m and mass 60g is suspended by two vertical wires at it's ends. A current of 5.0 A is set up in the rod through the wires.
Numerical 15
Two straight wires A and B of lengths 10m and 12m carrying currents of 4.0A and 6.0A respectively in opposite directions lie parallel to each other at a distance of 3.0cm. Estimate the force on a 15cm section of the wire B near its centre.
