## Introduction of Magnetic field

Subject: Physics

#### Overview

The magnetic field was discovered by Oersted in 1820. There are three rules in a direction of current and field they are; Right-hand thumb rule, Maxwell's corkscrew rule and Right hand first rule. Hall effect is a voltage is developed across the specimen in the direction perpendicular to the both the current and the magnetic field due to the applied magnetic field to a current carrying conductor and if a uniform magnetic field Bzis applied along the z-axis, it is found that an e.m.f. develops along the y-axis i.e. in a direction perpendicular to Ix and Bz. This voltage is called hall voltage. The magnetic field was discovered by Oersted in 1820. There are three rules in a direction of current and field they are; Right-hand thumb rule, Maxwell's corkscrew rule and Right hand first rule. Hall effect is a voltage is developed across the specimen in the direction perpendicular to the both the current and the magnetic field due to the applied magnetic field to a current carrying conductor and if a uniform magnetic field Bzis applied along the z-axis, it is found that an e.m.f. develops along the y-axis i.e. in a direction perpendicular to Ix and Bz. This voltage is called hall voltage.

### Introduction

Any connection between electric current and magnetism is the magnetic field which was made by Oersted in 1820. He placed a wire carrying current parallel to a compass needle on one occasion at the end of his lecture. To his surprise needle was deflected. The needle deflected in the opposite direction when reversing the current in the wire. Oersted concluded that the compass deflection was due to the magnetic field established around the current carrying conductor. The production of magnetism from an electric current which we call electromagnetism has opened the new era. The application of magnetic effects of electric current in one form to another operates all electrical machinery. We shall discuss the magnitude and direction of magnetic field due to various conductor arrangements and their practical applications in this Chapter.

Oersted Discovery

The Danish scientist Hans Christian Oersted discovered the magnetic effect of electric current in 1820. He performed a simple experiment which established the relationship between magnetism and electricity.

He found that when the large current was allowed to flow through a wire AB placed parallel to the axis of a magnetic needle kept directly below and sufficiently close to the wire, the needle was found to deflect from its normal position to as shown in the figure.(A). The deflection of a needle was found to be in the opposite direction on reversing the direction of the current by reversing the polarity of the battery as shown in fig(B).

This observation led Oersted to clarify that there must be some magnetic effect around the wire carrying electric current which deflected the magnetic needle. Thus, in the space around the conductor, an electric current produces the magnetic effect. In other words, the flow of electric charges in the source of magnetic field.

Direction of Current and Field

The magnetic field around a current carrying conductor and the direction of magnetic lines can be determined by the following rules.

(i) Right-hand thumb rule: To find out the direction of magnetic lines of force produced due to a straight current carrying conductor, this rule is used. According to this rule, if a current carrying conductor is imagined to be held in the right hand such that the thumb points in the direction of the current, then the tips of the curled finger encircling the conductor will give the direction of the magnetic lines of force. Fig (c)

(ii) Maxwell corkscrew rule ( Right handed screw rule):This rule is also used to find out the direction of magnetic lines of force produced due to a straight current carrying conductor. According to this rule, if the forward motion of an imaginary right-handed screw is in the direction of the current through a straight conductor, then the direction of rotation of screw gives the direction of the magnetic lines of force around the conductor as shown in Fig. (d)

(iii) Right-hand first rule: To find out the direction of magnetic lines of force produced due to a circular current carrying coil, this rule is used.According to this rule, if we curl the finger of the right hand in the direction of flow of current through the circular coil, then the direction in which the thumb points , gives the direction of magnetic lines of force. Fig(e)

The direction of magnetic field at any point is tangential to the magnetic lines of force.

### Hall effect

A voltage is developed across the specimen in the direction perpendicular to the both the current and the magnetic field due to the applied magnetic field to a current carrying conductor. This effect is called hall effect.

Consider a specimen in the form of rectangular cross section carrying current Ixin the x-direction . If a uniform magnetic field Bzis applied along the z-axis, it is found that an e.m.f. develops along the y-axis i.e. in a direction perpendicular to Ix and Bz. This voltage is called hall voltage.

Let us consider the situation before the magnetic field is introduced. There is an electric current flowing in the positive x-direction. When the magnetic field is introduced , the Lorentz force FLcauses the electrons to bend downward as shown in Fig. As a result, electrons accumulate on the lower surface producing a net negative charge there. Simultaneously, a net positive charge appears on the upper surface, because of the deficiency of the electrons. This combination of negative and positive surface charges create a downward electric field, which is called hall field.

The Lorentz force FLwhich produces the charge accumulation in the negative y-direction has the value,

$$F_L=ev_x B_z$$

or $$eE_H=ev_xB_z$$

or $$E_H=v_xB_z$$..(i)

From Ohm's law, current density(Jx) is written as

$$J_x=-nev_x$$..(ii)

Here, n be the number of electrons and negative sign is taken for electrons.

Dividing Eq. (i) by (ii)

$$\frac{E_H}{J_x}=\frac{B_z}{ne}$$

or $$E_H=-\frac{1}{ne}J_xB_z$$

Thus hall field is proportional to both current density and magnetic field. The proportionality constant that $\frac{E_H}{J_xB_z}$ is known as hall constant denoted by RH. So

Hall constant = $\frac{E_H}{J_xB_z}=\frac{1}{ne}$

$$R_H=\frac1{ne}$$

Now the hall constant or hall coefficient, RH is defined as the electric field strength produces per unit current density to the transverse magnetic field.

##### Things to remember
• In 1820, the Danish scientist Hans Christian Oersted discovered the magnetic effect of electric current.
• Oersted found that when large current was aalowed to flow through a wire placed parallel to the axis of a magnetic needle kept directly below and sufficiently close to the wire, the needle was found to deflect from its normal position.
• To find out the direction of magnetic lines of force produced due to a straight current carrying conductor, Right-hand thumb rule is used.
• Maxwell corkscrew rule is also used to find out the direction of magnetic lines of force produced due to a straight current carrying conductor.
• To find out the direction of magnetic lines of force produced due to a circular current carrying coil, Right-hand first rule is used.
• Hall effect is a voltage is developed across the specimen in the direction perpendicular to the both the current and the magnetic field due to the applied magnetic field to a current carrying conductor.
•  If a uniform magnetic field Bzis applied along the z-axis, it is found that an e.m.f. develops along the y-axis i.e. in a direction perpendicular to Ix and Bz. This voltage is called hall voltage.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.