Magnet Effect of Current Carrying Wire

The Oersted Experiment, conducted by Hans Christian Oersted in 1820, was a pivotal demonstration revealing the connection between electricity and magnetism.Oersted found that an electric current flowing through a wire generates a magnetic field around it. In his experiment, he placed a compass near a current-carrying wire and observed the compass needle's deflection when the current was activated.

1.0Oersted’s Experiments 

2.0Observation From The Experiment

• When a sufficient current flown through a wire positioned along the axis of a magnetic needle placed directly below it, the needle was observed to deflect from its usual position.
• The needle's deflection reversed direction when the current's polarity was switched by reversing the battery connection.
• The deflection of the magnetic needle varied with the strength of the electric current; as the current increased, the needle's deflection also increased, and vice versa.
• Oersted concluded that a magnetic field must surround the current-carrying wire, which was responsible for deflecting the magnetic needle..
• The movement of electric charges generates a magnetic field; the magnetism produced by electric current in a conductor is referred to as electromagnetism.

3.0Nature Of Magnetic Field

• The magnetic field close to a straight current-carrying conductor consists of concentric circles of magnetic field lines lying in a plane perpendicular to the conductor.
• The magnetic field near a current-carrying conductor is stronger and weakens as the distance from the conductor increases.
• The direction of the magnetic field at any given point is tangent to the magnetic field line at that point.
• The direction of the magnetic field lines, and therefore the magnetic field around a current-carrying conductor, is determined by

Right Hand Thumb Rule: It determine the magnetic field direction around a current-carrying conductor:                       

• Twist the fingers of your right hand in the direction of the current flowing through the loop; your thumb will then point in the direction of the magnetic field.

4.0Magnetic Field

• The area surrounding a current-carrying conductor, where its influence can be detected by a magnetic needle, is referred to as the magnetic field of the conductor.
• Magnetic Force is given by

$F=q(\vec{v}\times \vec{B})=qvB\mathrm{Sin}\theta$

• Dimensional Formula-$\left[M{L}^0{T}^{-2}{A}^{-1}\right]$
• SI Unit-Tesla
• CGS Unit-Gauss

Example: If a particle of charge q is moving with velocity v along y axis and the magnetic field B is acting along z axis, use the expression  $\vec{F}=q(\vec{v}\times \vec{B})$ to find the direction of force acting on it.

Solution:

$\vec{F}=q(\vec{v}\times \vec{B})$

$\vec{v}=v\hat{j}\text{ and }\vec{B}=B\hat{k}$

$\vec{F}=q(v\hat{j}\times B\hat{k})=qvB(\hat{J}\times \hat{K}$

$\vec{F}=qvB\hat{i}$, thus force acting on a particle along x axis

5.0Lorentz Force

When a charged particle having charge q  moves in a region, where both electric field

$\vec{E}$ and magnetic field $\vec{B}$ exists, it experiences a net force called Lorentz Force. 

$\vec{F}=q\vec{E}+q(\vec{v}\times \vec{B})=q(\vec{E}+(\vec{v}\times \vec{B})$

Example- What is the source of a magnetic force in a current carrying wire?

Solution: Moving electrons is the source of a magnetic force in a current carrying wire.

Example: Under what conditions can a proton pass through a magnetic field region without experiencing deflection?

Solution: When a proton moves either parallel or antiparallel to the direction of the magnetic field.

6.0Sample Questions On Magnet Effect On Current Carrying Wire

Q-1. Can a uniform magnetic field be used to speed up a charged particle ? Explain.

Sol. The force acting on the moving charged in the uniform magnetic field is $\vec{F}=\vec{v}\times \vec{B}$ , this force is always perpendicular to the motion of the particle and hence no work is done on the charged particle, Now work done=change in K.E, as no work is done, so change in K.E is zero and hence the charged particle can not speed up, although its direction of motion changes by the uniform magnetic field.

Q-2. In equation $\vec{F}=q\overrightarrow{(v}\times \vec{B})$, Which pairs are always perpendicular? Which pairs may have any angle between them?

Sol. $\vec{F}$ is always perpendicular to both $\vec{v}\text{ and }\vec{B}$, but both $\vec{v}\text{ and }\vec{B}$ have any angle between them.