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 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 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. 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 =
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 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
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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