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^Commonly used results in electricity & magnetism

^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

^Tangent galvanometer

^Tangent galvanometer

It is an instrument used to detect small currents using tangent law by keeping the magnetic needle at equilibrium under the torques of the Bcoil & BH.

The plane of the coil is set parallel to the magnetic meridian such that the magnetic needle points 0– 0 position. Now current to be measured is passed in the coil. The magnetic field produced by this current acts at right angles to the plane of the coil. Torque due to this field deflects the needle while the torque due to BH tends to restore the needle till the equilibrium is achieved. Let in equilibrium the magnetic needle makes an angle θ with the horizontal component of earth’s magnetic field, then we can write

Bcoil = BH tanθ

or    I = k tanθ

Here   is called reduction factor.

It is the amount of current required to produce a deflection of 450 in the magnetic needle. A tangent galvanometer is said to be both sensitive & accurate, if the change in its deflection is large for a given fractional change in current. The percentage error in the measurement of current is minimum when the deflection is 450.

^Dip (δ) & Horizontal component

^Dip (δ) & Horizontal component

The vertical component of the Earth’s magnetic field points downwards in the northern hemisphere. If the magnetic needle of a dip circle is perfectly balanced about a horizontal axis so that it dips (moves down) in a vertical plane of the magnetic meridian and aligns. Itself at some angle to horizontal at which are parallel, this angle is known as the angle of dip (also known as inclination).

We can say that angle of dip at a place in the magnetic meridian is the angle between horizontal component of earth’s magnetic field (H) & its resultant intensity (B) or it is the angle made by the axis of a freely suspended magnet with the horizontal line. e.g. Dip angle = 420  at Delhi.

In figure shown, the resultant magnetic field is in the magnetic meridian, d is angle of dip, BH and BV denote horizontal and vertical components of Earth’s magnetic field respectively.

BH = B cosδ, BV = Bsinδ

Exactly at the equator the Earth’s magnetic field is parallel to the Earth’s surface, angle of dip & vertical component of Earth’s magnetic field are zero, thus a freely suspended magnet will be horizontal at the equator. Exactly at the centre of poles the Earth’s magnetic field is normal to the surface of the Earth, angle of dip is 900 and the horizontal component of the Earth’s magnetic field is zero. Therefore a freely suspended magnet will become vertical at the poles.

^Dipole’s natural alignment

Dipole’s natural alignment

Any magnetic needle (or a dipole) free to move in a region of external magnetic field aligns so that its dipole moment become parallel to external magnetic field i.e. i.e. the position of stable equilibrium. This is because the position of stable equilibrium is the position of maximum stability or minimum potential energy.

^Superconductors: Perfect diamagnetics

Superconductors: Perfect diamagnetics

For super conductors cooled to very low temperatures χ = –1 & μr = 0.

Thus the super conductors are perfect diamagnetic materials. The phenomenon of perfect diamagnetism in superconductors is calledthe Meissner effect. In superconductors the field lines are completely expelled. Also a superconductor repels a magnet and (by Newton’s third law) is repelled by the magnet.

Superconducting magnets can be used in variety of situations, for example, for running magnetically levitated super fast trains.

Magnetic lines prefer to pass through air than through a diamagnetic material & through a ferromagnetic material than through air.

^Some more useful situations

Some more useful situations

1. The ratio of magnetic dipole moment to angular momentum for a uniformly charged configuration

2. A current loop behaves like a magnetic of dipole moment M = A N I, here I → current in loop, A → loop area & N → its no. of turns.

3. A current loop placed of dipole moment  in external uniform magnetic field  experiences a torque, .

4. A current carrying conductor placed in uniform magnetic field experiences a force.

5. For a closed loop of any shape net force on it is zero, however depending upon direction of current & external magnetic field a tension T = RBI may produce.

6. Two straight parallel conductors experience a force per unit of their length due to the magnetic field of each other.

^Oersted observation

Oersted observation

Oersted (1820) was the first to discover magnetic field associated with a current carrying conductor. He found that if a wire carrying a current from South to North is placed Over a magnetic needle, then the north pole the needle gets deflected towards the West. This is named as SNOW rule.

^What is a vector

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.

^Facts

Facts

  • If the liberated mass doesn’t react with electrodes, the electrode is called inert otherwise soluble.
  • Cu – anode with any metallic cathode in Cu –voltameter forms inert electrode.
  • Platinum electrodes in water voltameter, Platinum anode in Cu – voltameter are the examples of inert electrodes.
  • During electrolysis mass of cathode increases, (Reduction takes place at cathode) while that of anode decreases & concentration of electrolyte remains constant.
  • Alternating current can’t be used in electrolysis. As the frequency of AC changes periodically, so there will be no deposition on any electrode actually.
  • The back EMF or polarization EMF in water is 1.5 V. This is why to carry out electrolysis of H2O we need a voltage greater than 1.5 V.
  • Electrolysis is useful in, electroplating, extraction of metals from ores & their purification, electrolytic etching to mark logo, to produce H2 and O2 commercially, to separate non-metallic particles from the metallic ones, to ascertain the polarity of a battery, in finding equivalent weights & atomic weights.

*Physical quantities

*Physical quantities

Quantity (symbol) Definition / Relation Type
Mass (m) Quantity of matter contained in a substance Scalar
Distance (D) Actual path length Scalar
Speed (v) Distance covered per unit time spent Scalar
Time (t) Reference to measure duration of an event. Scalar
Electric current (I) Rate of flow of charge. Scalar
Pressure (P) Normal force per unit area Scalar
Surface tension (S) Tangential force per unit length Scalar
Work (W) Line integral of force Scalar
Power (P) Rate of work Scalar
Energy (E) Capacity to do work Scalar
Heat (H) Energy in transit due to temperature difference Scalar
Electric potential (V) Line integral of electric field Scalar
Electric flux (f) Surface integral of electric field Scalar
Specific heat (s) Heat per unit temp. change per unit mass Scalar
Latent heat (L) Heat per unit mass for changing state of a material Scalar
Temperature (T) Degree of hotness or coldness Scalar
Electric charge (q) Measure of amount of electrification Scalar
Density (r) Mass per unit volume Scalar
Moment of inertia (I) Reluctance for rotational changes Scalar

 

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