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^Commonly used results in electricity & magnetism

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^Commonly used results in electricity & magnetism

Electricity Magnetism
Source of field Static or moving charges Moving charges
SI units Charge: coulomb (C)Electric field: Newton /coulomb (N/C) Magnetic pole: ampere meter (Am).Magnetic field is tesla (T)
Field lines Discontinuous: Start at a + ve charge & end at equal -ve charge. Continuous: Have no start or end & are closed loops.
Field due to a mono pole
Proportionality constant

(SI units) ke = 1 in cgs units

   in SI unitskm = 1 in cgs units
Force on a monopole
Potential due to a mono pole
Coulomb’s law of two point poles
Screening or shielding Using hollow metallic boxes. Using ferromagnetic boxes.
Gauss’s law
Force exerted by field on charge particles
Trajectories of charged particles in field In electric field:

1.  Straight line if the angle between electric field & velocity of the charges particle is 00 or 1800 &

2.  parabolic if the angle between electric field & velocity of the charges particle is other than 00 & 1800.

 In magnetic field:

1.    Straight line if the angle between magnetic field & velocity of the charges particle is 00 or 1800,

2.    circular if the angle between magnetic field & velocity of the charges particle is 900.

3.    helical if the angle between magnetic field & velocity of the charges particle is other than 00, 900 & 1800.
Dipole moment of a dipole of length 2 L
Field on axial line of a dipole
Field on equatorial of a dipole
Field at any point of short dipole
Potential on the axial line of dipole
Potential at any point of short dipole
Force on a dipole placed in a region of uniform field Force on each pole = qE

Net force on dipole = 0

 Force on each pole = mB

Net force on dipole = 0
Force on a dipole placed in a non uniform field
Torque acting on dipole placed in a region of uniform field
Condition for equilibrium of dipole placed in a region of uniform field
Potential energy of dipole – field system placed in a region of uniform field

^Vibration magnetometer

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^Vibration magnetometer

A magnet free to vibrate about vertical axis passing through its CM is first kept in a non- magnetic hook along BH.

On deflecting it slightly by an amount θ, it experiences a restoring torque due to horizontal component of earth’s field BH

τ = M BH sinθ

≈M BH θ   [As sinθ ≈ θ, for small angle deflection.

Due to inertia of the magnet it start oscillating simple harmonically. We know from the theory angular SHM that linear frequency, angular frequency & time period of oscillations is,

Thus for this situation we have

Here, I = MI of the magnet

Uses:

For two dissimilar magnets using

Here Ts = time period for the sum position & Td = time period for the difference position.

^Compass & dip circle

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^Compass & dip circle

A compass needle consists of a magnetic needle is free to swing (oscillate or deflect) in a horizontal plane about a vertical axis.

A compass needle when placed in a horizontal plane & free to move aligns itself parallel to BH.

At the poles, the magnetic field lines are vertically so that the horizontal component is negligible & the compass needle can point along any direction & thus can’t be used as a direction finder. In that case we use a dip circle.

^Magnetic elements of earth

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Magnetic elements of earth

Declination (θ), Dip (δ) &  Horizontal component (BH) are called magnetic elements of earth as earth’s magnetic field can be completely defined in both magnitude & direction by knowing these three.

^Geomagnetism

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Geomagnetism

1. Study of magnetic field of earth is called Geomagnetism or terrestrial magnetism.

2. William Gilbert (in about 1600) was the first to demonstrate that the entire earth behaves as an enormous magnet.

3. The magnitude & direction of Earth’s magnetic field can be obtained approximately by assuming that the earth has a magnetic dipole of dipole moment about 8 x 1022 J/T located at its centre tilted 11.5O from the spin axis of the earth as shown in the diagram.

4. The average strength of the earth’s magnetic field is about half a Gauss. Also Bequator = 30 μT, Bpole = 60 μT. Range of magnetic field is about 5 R from the radius of earth.

5. Earth’s mag. field changes both in magnitude & direction with the time. It is fairly constant over a span of few years but noticeable changes occur in say 10 yrs.

^Motional emf

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Motional emf

No motional emf will be produced across the conductor if any two vectors are parallel to each other.

Polarity of the emf can be checked knowing the direction of drift of electrons using .

 

 

 

^Biot–savart’s law

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Biot–savart’s law

The magnitude of the magnetic field produced depends upon

  1. strength of current flowing in the conductor
  2. shape, size of conductor &
  3. position of observation point where the field is to be calculated.

Direction of magnetic field due to both straight as well as curved conductor can be calculated by right hand stretched thumb rule. For straight conductor thumb point current & curl of fingers point magnetic lines while in a curved conductor reverse of it. On reversing the direction of current the direction of magnetic field produced is reversed.

^What is a vector

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Description of motion along a straight line the role of direction is played by +ve & -ve signs of that direction, however to describe motion in 2 & 3 dimensions we need vectors.

^What is a vector

If both magnitude and direction are required to completely described a physical quantity, then it is called a vector. A vector quantity is  represented by putting on arrow above it or by bold letter e.g. it Q is vector then we represent it as  or Q. If a quantity can have any direction it is called polar vector. If its direction is along axis (axis of rotation), then called axial vector.

^Thermoelectric effect

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Thermoelectric effect

Consider an metal rod heated at one end & cooled at the other end as shown.

The electrons in the hot region are more energetic and therefore have greater velocities than those in the cold region. Consequently there is a net diffusion of electrons from the hot end towards the cold end which leaves behind positive metal ions in the hot region and accumulated electrons in the cold region. This situation prevails until the electric field developed between the positive ions in the hot region and the excess electrons in the cold regions prevents further electron motion from the hot to cold end. A voltage developed between the hot and closed ends with the hot end at positive potential at the steady state.

This effect in which a temperature gradient between two points in a material (may be a conductor or semiconductor) gives rise to a built in electric field or a voltage difference between two points. This phenomenon is called the Seebeck effect or the thermoelectric effect.

 

^General

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^General

QUANTITY SYMBOL DEFINITION/RELATION SI UNITS DIMENSIONS
Mass M or m Also called inertia. kg [M]
Area A or S Region bounded by lines or curves in 2D. M2 [L2]
Volume V Space bounded by lines or curves in 3d. m3 [L3]
Density r Mass per unit volume kg m – 3 [ML – 3]
Linear density m Mass per unit length kg m – 1 [ML – 1]
Surface density s Mass per unit area kg m – 2 [ML – 2]
Specific volume 1/r Volume per unit mass kg – 1 m 3 [M – 1 L3]
Number density n Number of particles per unit volume. m– 3 [L– 3]
Specific gravity Or relative density SG density of body /density of water at 4 0C no units no dimensions

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