Magnetic Effect Of Electric Current Flashcards
State Ampere’s law
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The line integral of magnetic field of induction B around any closed path in free space is equal to the absolute permeability of free space (μ0) time the total current flowing through the area bounded by that part.
Expression for force on a conductor carrying current
F = il x B
F=iBlsinθ
Mathematical expression for Ampere’s law
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Line integral B.dl = μ0i = line integral Bdl*cosθ
Magnetic field due to long straight conductor carrying current - Derivation
Infinitely long, straight, conductor Imaginary circle with r as radius perpendicular to straight conductor. θ=0 B is same at all points (symmetry) B= (μ0/4π)*(2i/r)
Magnetic field due to long straight conductor carrying current - Expression
B= (μ0/4π)*(2i/r)
Magnetic induction along the axis of a long straight solenoid - Derivation
Rectangular path ABCD L= length of solenoid n= no of turns per unit length Total current = nLi Split line integral into four parts (each side) DC too far = 0 AD and BC perpendicular = 0 B= μ0ni
Expression for magnetic field well inside a solenoid
B= μ0ni
Magnetic induction at a point near the end of a solenoid - expression
B= (1/2)*μ0ni
Magnetic induction along the axis of a toroid- Derivation
N= no of turns Total current= NI B=μ0Ni / 2πr If n= no of turns per unit length B= μ0ni Pg 234
Magnetic induction along the axis of a toroid- expression
N= no of turns Total current= NI B=μ0Ni / 2πr If n= no of turns per unit length B= μ0ni
What is a toroid?
Toroid is a solenoid bent into the shape of a hollow doughnut.
What is a galvanometer?
Galvanometer is a device with the help of which a very small electric current can be detected.
Two types of Moving Coil Galvanometers
Suspended coil type
Pivoted coil type
Construction of MCG
Light rectangular coil of thin insulated wire with many turns wound on a non-magnetic frame of aluminum (or copper).
Coil is suspended freely so that it can rotate freely in uniform radial magnetic field set up between two strong poles of horse-shoe magnets which is having cylindrically concave pole pieces and soft iron cylinder.
Rectangular coil suspended by means of a thin phosphor bronze wire suspension.
Small plane mirror is fixed on phosphor bronze fibre- used in lamp and scale arrangement
Other end of coil connected to phosphor bronze helical spring and serves the purpose of leading current in and out of the coil.
The elastic behavior of helical spring helps the coil to bring back to its original position when current is cut-off.
Why is a soft iron cylinder used as a core in an MCG?
Makes field radial
Increases magnetic flux
State the principle of MCG
When a coil carrying electric current is suspended in a uniform magnetic field, a torque acts on it which tends to rotate the coil about the axis of suspension so that the magnetic flux passing through the coil is maximum.
Expression for deflecting torque of an MCG
τd= nBiA
What does the deflecting torque on an MCG depend on?
Directly proportional to :
Magnetic induction of magnetic field in which the coil is suspended.
Current flowing through the coil.
Constants if the coil (effective area and number of turns)
How does a MCG work?
Deflecting torque= force * perpendicular distance
Torque causes pointer attached to the coil to deflect and move on graduated scale.
What does the restoring torque depend on? (MCG)
Directly proportional to deflection of coil.
τ=cθ
What in an MCG provides restoring torque?
Twist in phosphor bronze fibre
Expression for current flowing through the coil of an MCG
i= θ(c/nBA)
How does the current flowing through the MCG depend on the angle of deflection of the coil?
Directly proportional
Advantages of MCG
Not affected by strong magnetic field
Have high torque/weight ratio
Very accurate and reliable
Scales are uniform
Disadvantages of an MCG
Change in temperature affects restoring torque
Restoring torque cannot easily be changed
Possibility of damage of phosphor bronze fibre suspension and helical spring arising out of severe stress.
Cannot be used for AC.
What can a PMMCG be modified as?
Ammeter
Voltmeter
Ballistic galvanometer
Why is an ammeter required in some cases instead of a galvanometer?
Spring and moving coil very delicate
Full scale deflection for current of the order of 10mA (limiting value)
If larger current is sent through, MCG may get damaged
What is a shunt?
When a current larger than 10mA is to be measured by a MCG, low resistance is connected in parallel with the MCG which is called shunt.
What are shunt resistances made up of? Give reasons
Magnanin
Negligible temperature coefficient of resistance.
How does a shunt resistance work?
Bypasses most of the current and allows smaller current to flow through coil of MCG
Define Ammeter
A shunted permanent magnet moving coil galvanometer (PMMCG) is called an ammeter.
Expression for value of shunt resistance
igG=isS
S= (ig/(i-ig))*G
What are the functions of a shunt resistor?
Increases the effective resistance of an ammeter.
Increases the range of instrument.
Provides an alternative path for excess current to pass which protects the galvanometer from damage.
Expression for current flowing through shunt resistance
is=(G/(S+G))*i
What is an ideal ammeter?
Zero resistance
What is a practical ammeter?
Finite and small resistance.
What is manganin?
Alloy of cooper, manganese and nickel
What is a voltmeter?
A permanent magnet moving coil galvanometer (PMMCG) instrument in series with a high resistance is called a voltmeter.
Why is a resistance connected in series with a PMMCG for a voltmeter?
MCG is very delicate and can give full scale deflection for current of the order 10mA or when a small pd is applied across its terminals. So, to measure large p.d., effective resistance of instrument should be high.
If large pd is applied across galvanometer, large current will pass through MCG which may result in burning of coil due to excessive heat.
What is an ideal voltmeter?
A voltmeter that has infinite resistance, so that when it is connected between two points in a circuit, it would not change the value of current, is known as an ideal voltmeter.
Expression for resistance to be connected in series.
V= ig(G+Rs) Rs= (V/ig)-G
Functions of a high value series resistor
To increase effective resistance of a galvanometer.
To increase range of voltmeter.
To protect galvanometer from damage due to large current.
What is meant by sensitive galvanometer?
An MCG is said to be sensitive if it gives larger change in deflection for smaller change in current.
Expression for sensitivity of an MCG
Si= dθ/di= nBA/c
What factors does the sensitivity of an MCG depend on?
Number if turns of the coil
Magnetic induction of magnetic field
Area of rectangular coil
Twist constant of phosphor bronze wire.
How can we increase the sensitivity of an MCG?
Increasing the number of turns ‘n’ of the coil
Increasing the magnetic induction ‘B’ by using a strong magnet
Increasing area of coil ‘A’
Decreasing/minimizing the restoring torque per unit angular displacement ‘c’
Elaborate : there is a limit to increase sensitivity of an MCG
Stronger horseshoe magnet= instrument bulky
Increase no of turns and area of coil= May coil heavy= suspension fibre may not be able to support it= thick suspension fibre used= decreases sensitivity
To minimize this constant= flat strip of phosphor bronze wire should be taken to suspend the coil.
What is meant by accuracy of an MCG?
An MCG is said to be accurate if the relative error in the measurement of current is less and vice versa.
Expression for accuracy of an MCG
di/i = dθ/θ
What is a cyclotron?
Cyclotron is a circular particle accelerator which uses magnetic field to bend charged particles into a circular path and electric field to accelerate them to high velocities.
Principle of a cyclotron
Positively charged particle moves with a definite periodic time again, and again, perpendicular to uniform magnetic field and is accelerated repeatedly by high frequency electric field and traces a spiral of increasing radius.
Construction of a cyclotron
Two d-shaped semicircular, hollow metal boxes - dees
Small gap between two dees kept in space between two pole pieces of huge electromagnet (capable of producing very high magnetic field) perpendicular to the plane of dees.
Alternating potential and high frequency applied between the dees. Size is compact.
Dees enclosed in a cylindrical evacuated chamber. Evacuated chamber along with dees placed between poles of a strong magnet.
Working of cyclotron
pg 241
Radius of semicircle traced by positive ion in the cyclotron
r= mv/(Bq)
Expression for time required for an ion to traverse semicircle
t= πm/(Bq)
Time period of ions in a cyclotron- expression
T= 2πm/(qB)
Expression for Magnetic resonance frequency
f= qB/(2πm)
KE if ion in a cyclotron- expression
KE= qqBBR*R /2m
Limitations of cyclotron
Cannot accelerate uncharged particles like neutrons
Cannot accelerate electrons as they have a very small mass and move with a very high speed.
Charged particles cannot move without speed beyond a certain limit in Cyclotron.
It is not possible to design a machine capable of producing highly energetic particles having energy of the order of 500 MeV
Why can’t a cyclotron accelerate electrons?
Electrons have very small mass = high speed = cannot remain in phase with field.
