Electromagnetism - Part 1: Theory and Definitions - Lorentz force, Biot-Savart Law, Ampere’s Force Law, Electromagnetic Induction, Self and Mutual Induction

Here's a quick outline of the topics which will be introduced in this tutorial:

Electromagnetism - Part 1: Theory and Definitions - Lorentz force, Biot-Savart Law, Ampere’s Force Law, Electromagnetic Induction, Self and Mutual Induction

Target Audience: High School Students, College Freshmen and Sophomores, students preparing for the International Baccalaureate (IB), AP Physics B, AP Physics C, A Level, Singapore/GCE A-Level; 

Class 11/12 students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE/AIEEE Anyone else who needs this Tutorial as a reference!


Lorentz force

The total Electromagnetic force on a moving charge, called Lorentz force is given by F = q E + q[v × B] where B is the magnetic force intensity vector which characterizes the magnetic force. The above law is universal, i.e, it is applicable even for varying electric and magnetic fields and for all velocities of the moving charge.

Biot-Savart Law

Helps you asses the magnetic field intensity created by a moving charge.

Basic Laws of Magnetic Field and their applications
• Gauss theorem for B: The Flux of B through any closed surface is zero
• Theorem on circulation of B or Ampere’s Circuital Law
• Theorem on circulation of B is used to calculate magnetic fields in symmetric situations like long straight conductor, infinitely long solenoid, toroid, large current carrying plane etc. using the symmetry.

Ampere’s Force Law

The force acting on a current carrying conductor in a magnetic force is called Ampere’s force

Electromagnetic Induction

• The phenomenon of electromagnetic induction states that an induced current appears in a closed conducting loop when the magnetic flux enclosed by the loop is changed.
• Lenz Law : It states that the induced current is directed such that it’s magnetic flux opposes the original change in magnetic flux.
• Faraday’s Law of EMI : The e.m.f induced in a loop, whatever the cause of it, is given as ξi = − dφ/dt measured in Weber/s.
• e.m.f is caused by time-variant magnetic field or by the motion of loop in a space-variant magnetic field.

Self and Mutual Induction

• The process of variation of current in a circuit leading to induced e.m.f. in the circuit is called Self Induction.
• φ = LI, where L is the inductance of the circuit, which depends on the shape and size of the loop, measured in Henry.
• The presence of magnetic coupling between two circuits leads to Mutual Induction. e.m.f. is induced in one circuit due to change in current in other circuit.

Here are some of the problems solved in this tutorial :

Q: Consider a long straight uniform cylinder of radius R. A direct current of density J flows along the length of cylinder. A cylindrical cavity of radius r is carved out from the cylinder as shown in the cross-section. Find the magnetic field in the cavity.

Q: In the figure shown, a coil of single turn is wound on a sphere of radius r and mass m. The plane of coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If sphere is in rotational equilibrium, Find the value of B. Let i be the counter-clockwise current through the coil when observed from the top.

Q: Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having it’s center at the origin of the co-ordinate system. If current I flows through each ring, find the magnitude of magnetic field at the common center i.e, origin.

Complete Tutorial with Solved Problems :

In case you'd like to look through our other tutorials on Electrostatics and Electromagnetism :

 Electrostatics - Part 1: Theory, definitions and problems
 Columb's law. Electric Field Intensity, principle of superposition, gauss theorem, electrostatic potential, electric field intensities due to common charge distributions, capacitors and calculating capacitance. Solved problems.  

Electrostatics - Part 2: More solved problems.
More solved problems related to the concepts introduced above. 
Electromagnetism - Part 1: Theory and Definitions
 Lorentz Force, Bio-Savart law, Ampere's force law, basic laws related to Magnetic fields and their applications. Magnetic field intensities due to common current distributions. Electromagnetic Induction. Self and mutual induction. 
Electromagnetism - Part 2: Solved problems
Solved problems related to the concepts introduced above. 
 Advanced concepts in Electrostatics and Electromagnetism ( Theory only )
Advanced concepts related to electrostatics and electromagnetism (theory only).