A moving charge produces both electric field and magnetic field and both magnetic field can exert force on it.

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Todd Cobb
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1 Key Concepts A moving charge produces both electric field and magnetic field and both magnetic field can exert force on it. Note: In 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field. Biot- Savart Law Magnetic induction produced by a current Biot-Savart Law The magnitude of db is proportional to sine, where 0 is the angle between the vectors ds and The observations are summarized in the mathematical equation called the Biot-Savart law (magnetic field due to the current-carrying conductor) Magnetic Field Generated by Current in Straight Wire Consider a field point P that is a distance R. from the axi 1 P a g e

Graph showing variation of B with respect to r Magnetic field due to straight wire A Long Straight Conductor The thin, straight wire is carrying a

Conducto r If the conductor is an infinitely long, straight wire 1 = π/2 and 2 = - π/2 So equation becomes : Solenoid A solenoid is a coil of wire

2 Graph showing variation of B with respect to r Magnetic field due to straight wire A Long Straight Conductor The thin, straight wire is carrying a constant current Due to long st. Conducto r If the conductor is an infinitely long, straight wire 1 = π/2 and 2 = - π/2 So equation becomes : Solenoid A solenoid is a coil of wire carrying an electric current. The magnetic field is similar shape to that around a bar magnet. The strength of the field increases with 1. the electric current 2. the number of turns in the coil Solenoid For a solenoid of length L with current i: B = u 0 NI/L 2 P a g e

Toroid The toroid has N turns of wire Field at appoint at distance r from center of toroid (loop1) Toroid There is no field outside the coil(loop2) Current carrying sheet Thick Sheet

s magnetic field Gilbert s Magnetism (Earth magnetic Field) The line of earth s magnetic induction lies in a vertical plane coinciding with the magnetic North South direction at that place.

3 Toroid The toroid has N turns of wire Field at appoint at distance r from center of toroid (loop1) Toroid There is no field outside the coil(loop2) Current carrying sheet Thick Sheet Magnetic Induction due to current carrying Sheet B = ½ 0I Where I = Linear current density(a/m) Magnetic Induction due to Thick Sheet B out = ½ 0Id B in = ½ 0Jx Current density JA/m 2 Earth s magnetic field Gilbert s Magnetism (Earth magnetic Field) The line of earth s magnetic induction lies in a vertical plane coinciding with the magnetic North South direction at that place. Earth s magnetic axis is slightly inclined to the geometric axis of earth and this angle varies from 10.5* to 20*(in degree) The earth magnetic poles are opposite to the geometric poles. 3 P a g e

At a given place on the surface of earth, the magnetic meridian and the geographic meridian may not coincide. The angle between them is called Declination at that place.

Amperes Law The magnetic field in space around an electric current is proportional to the electric current which serves as its source.

4 At a given place on the surface of earth, the magnetic meridian and the geographic meridian may not coincide. The angle between them is called Declination at that place. Let B = total magnetic induction of the earth at that point B v = the vertical component of B in meridian plane = B B H = the horizontal component of B in meridian plane = B Ampere s Law Therefore = Amperes Law The magnetic field in space around an electric current is proportional to the electric current which serves as its source. Equation: Earth s magnetic Field Lorentz Force Lorentz Force Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force. Motion of A charge in uniform magnetic field 4 P a g e When v is to B : motion will be in a st.line and F = 0 When v is perpendicular to B: Motion will be in circular path with radius R=mv/qB and angular velocity =

5 qb/m and F = qvb When v is at angle to B : motion will be helical with radius with R = mvsin /qb Pitch 2 mvcos /qb and F = qvbsin Magnetic force on a st. current carrying wire L = length of conductor in direction of current in it. B = magnetic induction. In general: F = S Magnetic interaction force between two parallel long straight currents Repulsion, if current are anti- parallels Attraction, if current are parallels 5 P a g e

Magnetic Torque on a closed current circuit Note: this expression can

Moving coil Galvano meter Moving coil Galvanometer Deflecting torque (T

magnetic field: Magnetic force on a loop in a uniform B is zero Force

6 Magnetic Torque on a closed current circuit Note: this expression can be used only if B is uniform otherwise calculus will be used. Moving coil Galvano meter Moving coil Galvanometer Deflecting torque (T d ) = restoring torque(t r ) Force on random shaped conductor in magnetic field: Magnetic force on a loop in a uniform B is zero Force experienced by a wire of any shape is equivalent to force on a wire s end point. 6 P a g e

7 Magnetic moment of a rotating charge If a chare is rotating at angular velocity w, It equivalent current is given as I =, and its magnetic moment is M = 1/2q R 2. Extra : Note: The rate of magnetic moment to angular momentum of a uniform rotating object which is charged uniformly is always a constant. irrespective of the shape of conductor M/L = q/2m 7 P a g e

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Magnetic field and magnetic poles

Magnetic field and magnetic poles Magnetic Field B is analogically similar to Electric Field E Electric charges (+ and -)are in analogy to magnetic poles(north:n and South:S). Paramagnetism, Diamagnetism,