Moving Charges and Magnetism
4.1 Introduction
In 1820, Danish physicist Hans Christian Oersted firstly demonstrated that both electricity and magnetism are closely related to each other.This led to unification of electricity and magnetism.The branch of physics as a result of the unification of electricity and magnetism is known as electromagnetism.Thus, the magnetism due to the electric current in a conductor is called electromagnetism.
Explain Oersted's experiment to show the magnetic effects of electric current.
In 1820, Danish scientist Hans Christian Oersted discovered that electric current produces a magnetic effect.
Experiment
A straight wire was placed above a magnetic compass needle.
When no current flowed through the wire, the needle pointed in the North–South direction as usual.
When electric current was passed through the wire, the compass needle deflected (turned) from its normal position.
Observations
1. The needle deflected when current flowed.
This showed that a current-carrying wire affects a magnetic needle.
2. Reversing the current reversed the deflection.
When the battery connections were reversed, the current flowed in the opposite direction. As a result, the compass needle deflected in the opposite direction.
3. Stronger current caused greater deflection.
Small current → small deflection
Large current → large deflection
This means the strength of the magnetic effect increases with current.
Conclusion
Oersted concluded that:
“An electric current produces a magnetic field around a conductor.”
In other words:
- Moving electric charges (current) create a magnetic field.
- The flow of electric charges is the source of magnetism around the wire.
Ampere's Swimming Rule ( SNOW Rule ) :
The SNOW Rule is used to determine the direction of deflection of a magnetic needle near a current-carrying conductor.
SNOW stands for:
S → South pole
N → North pole
O → Over the wire (current coming out of the page toward you)
W → Under the wire (current going into the page away from you)
Rule:
- If current flows Over the wire (out of the page), the North pole of the magnetic needle deflects toward the West ( In fig.a).
- If current flows Under the wire (into the page), the North pole of the magnetic needle deflects toward the East( In fig.b ).
Nature of Magnetic Field
Figure A – Iron Filings Experiment
Ek straight wire ko cardboard ke through pass kiya gaya hai.
Wire me current flow karaya jata hai.
Cardboard par iron filings (lohe ka burada) spread kiya jata hai.
Iron filings wire ke around gol-gol circles (concentric circles) bana leti hain.
Jisse ye conclusion milta hai ki current carrying wire ke around circular magnetic field banta hai.
Figure (B): Current Downward (⊗)
The symbol ⊗ means current is going into the paper (away from us).
The magnetic field lines are clockwise.
The north pole of the magnetic needle p
oints along the clockwise direction.
oints along the clockwise direction.
Figure (C): Current Upward (⊙)
The symbol ⊙ means current is coming out of the paper (towards us).
The magnetic field lines are anticlockwise.
The north pole of the magnetic needle points along the anticlockwise direction.
Thus, the magnetic field around a current carrying straight conductor consists of concentric circles of magnetic field lines lying in a plane which is at right angles to the current carrying conductor ( figure.4).
Magnetic field near the current carrying conductor is stronger and becomes weaker as the distance from the conductor increases.
The direction of magnetic field at any point is along the tangent to the magnetic field line at that point, and it can be determined by any of two rules :
A) Right handed screw rule ( Maxwell's Cork Screw Rule ) : If the forward motion of an imaginary right handed screw is in the direction of the current through a linear conductor,then the direction of rotation of the screw gives the direction of the magnetic lines of force around the conductor ( fig. )
B) Right hand thumb rule : If a conductor carrying current 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 fingers encircling the conductor will give the direction of the magnetic field lines ( fig.).
4.2 Magnetic Field and Magnetic Force
Magnetic Field : A magnetic field is the space around a magnet where its magnetic force acts. Strength of magnetic field ( B ) is also known as magnetic flux density or magnetic induction or magnetic vector.
Note : Electric force on a charge accelerates or retards the charge, but magnetic force on a charge reflects the path of the charge.
Earth ' s magnetic field is about 3.6 × 10^ (-5) T
Lorentz Force : When a charged particle moves in a region, where both electric field and magnetic field exist, it experiencesa net force called Lorentz force.
Lorentz force = Force on charge due to electric field + force on charge due to magnetic field.
Fleming 's Left Hand Rule :
Stretch the left hand such that the fore - finger, the central finger and the thumb are mutually perpendicular to each other. When fore - finger points in the direction of magnetic field and central finger points in the direction of current, then the thumb gives the direction of the force acting on the conductor.
Differentiate between electric field and magnetic field :
Electric field
- Electric field is produced by a static as well as moving electric charge.
- Electric field exerts a force on a stationary as well as on a moving electric charges.
- The path followed by the charged particle is parabolic.
- Electric field depends upon permittivity of a material.
Magnetic field
- Magnetic field is produced by moving charges.
- Magnetic field exerts a force on moving charges only.
- The path followed by the charged particle is circular.
- Magnetic field depends upon permeability of a material.
Find an expression for magnetic force on a current carrying conductor placed in uniform magnetic field.
Derive following expressions for charged particle moving in uniform magnetic field in different cases . i) radius of circular path ii) Time period and frequency.
Case 1. When motion of charged particle is parallel or antiparallel to the magnetic field. In this case moving charges particle does not experience any force.
Case II. When charged particle moves at right angle to the magnetic field.
Case III. When the charged particle moves at an angle to the magnetic field ( other than 0, 90 and 180 degree ).
Explain a velocity selector or velocity filter. What are the uses of velocity selector ?
Velocity selector is a set up to select charged particles of a particular velocity from a beam passed through a space having crossed electric and magnetic fields.
Mutually perpendicular electric and magnetic fields are called crossed fields.
Uses of Velocity Selector :
This method can be used to measure specific charge.
Mass Spectroscopy works on the principle of velocity selector.It is a device used to separate ions according to their specific charge
What is a cyclotron ? What is the principle, construction, working and theory of cyclotron ? What are the limitations, uses and functions of electric and magnetic fields in cyclotron ?
A cyclotron is a device used to accelerate charged particles (such as protons, deuterons, and alpha particles) to very high speeds using electric and magnetic fields.
Principle of Cyclotron
A cyclotron works on the principle that a charged particle moving perpendicular to a uniform magnetic field follows a circular path, and an alternating electric field applied at the proper frequency accelerates the particle repeatedly, increasing its energy.
Construction of Cyclotron
The main parts of a cyclotron are:
- Two D-shaped hollow metal chambers (Dees) – placed facing each other.
- Strong electromagnet – produces a magnetic field perpendicular to the Dees.
- High-frequency alternating voltage source – provides electric field between the Dees.
- Ion source – placed at the center to produce charged particles.
- Target – where the accelerated particles finally strike.
Working of Cyclotron
Charged particles are produced at the center by the ion source.
The magnetic field makes the particles move in a circular path inside a Dee.
When the particles reach the gap between the Dees, the electric field accelerates them.
Their speed increases, so the radius of the circular path becomes larger.
The particles move in a spiral path, gaining energy each time they cross the gap.
When they reach the outer edge, they are extracted and directed toward the target.
Conclusion
A cyclotron is a device that accelerates charged particles using a combination of magnetic field (for circular motion) and electric field (for acceleration). It is used in nuclear physics research and in the production of medical isotopes.
Limitations
i) Cyclotron cannot accelerate uncharged particles like neutron.
ii) Cyclotron cannot accelerate electrons because they have very small mass .
Uses of a Cyclotron
i) It is used to produce radioactive material for medical purposes ( diagnostics and treatment of chronic diseases ).
ii) It is used to synthesize fresh substance.
iii) It is used to improve the quality of solids by adding ions.
iv) It is used to bombard the atomic nuclei with highly accelerated particles to study the nuclear reactions.
State and derive an expression for Biot Savart's law.
Biot Savart's law is used to determine the strength of the magnetic field at any point due to a current carrying conductor.
Consider a very small element AB of length dl of a conductor carrying current I. The strength of magnetic field dB due to this small current element at a point P, distance r from the element is depends upon :
Application of Biot - Savart's Law
i) Magnetic field due to infinity long straight wire .
