9. Electromagnetic Induction By Sanjay Pandey

1

1.    2.

9. Electromagnetic Induction

Electromagnetic Induction If an electric current produces a magnetic field, then a magnet should be able to generate an electric current. A current is produced in a wire when there is relative motion between the wire and a magnetic field. Such a current is called an induced current . This effect is called electromagnetic induction (discovered by Michael Faraday). The strength of the current depends on the magnetic field strength and the wire’s speed. Magnetic flux

Magnetic flux, 𝛷𝛷, represents a quantity of magnetic force lines passing through a given area. The number of magnetic force lines increases if we have a stronger field or if the area enclosed is larger. �⃗, perpendicular to the plane of the loop Therefore, 𝛷𝛷 = 𝐵𝐵⊥ 𝐴𝐴. Where 𝐵𝐵⊥ is the component of B In SI units, flux is measured in webers (Wb) and is calculated from 𝛷𝛷 = 𝐵𝐵⊥ 𝐴𝐴 with B measured in Tesla and A in meters squared. It is important to note that only the component of the magnetic field perpendicular to the area is used in the calculation. Thus, in general, 𝛷𝛷 = 𝐵𝐵𝐵𝐵 cos 𝜃𝜃 where 𝜃𝜃 is the angle between the magnetic field and the normal to the area. R

Suppose we have a magnetic field going through a surface. Then the perpendicular component of the magnetic field going through the surface times the area of the surface is called the magnetic flux. General Expression: �⃗. 𝑑𝑑𝐴𝐴⃗ 𝜙𝜙 = ∫ 𝐵𝐵

Simple case 1: uniform 𝐵𝐵⊥ surface: 𝛷𝛷 = 𝐵𝐵𝐵𝐵 Simple case 2: surface is closed: Φ = 0 3.

Faraday’s Law

𝑑𝑑𝑑𝑑

𝜀𝜀 = − 𝑑𝑑𝑑𝑑 The emf induced in any loop or circuit is equal to the negative rate of change of the magnetic flux through that loop.

Fig. 1. Voltmeter reading gives rate of change of the number of lines linking the loop.

2 4.

Lenz’s Law

𝑑𝑑𝑑𝑑

𝜀𝜀 = − 𝑑𝑑𝑑𝑑 The direction of the induced emf is such as to create a current which will oppose the change in the flux.

Faraday’s Law: General Form

Fig.2. Motion as shown produces clockwise current which makes B field opposing the increase.

� 𝐸𝐸�⃗ . 𝑑𝑑𝑆𝑆⃗ = −

𝐶𝐶

↑ ε

𝑑𝑑 �⃗. 𝑑𝑑𝐴𝐴⃗ � 𝐵𝐵 𝑑𝑑𝑑𝑑 𝐶𝐶

↑ ϕ

3