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Magnetic Fields
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Magnetic Fields and Forces a single magnetic pole has never been isolated magnetic poles are always found in pairs Earth itself is a large permanent magnet
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Magnetic Fields and Forces
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We can represent the magnetic field ( ) by means of drawings with magnetic field lines We can define a magnetic field at some point in space in terms of the magnetic force that the field exerts on a charged particle moving with a velocity Magnetic poles exert attractive or repulsive forces on each other and that these forces vary as the inverse square of the distance between interacting poles
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Magnetic Fields and Forces The magnitude F B of the magnetic force exerted on the particle is proportional to the charge q and to the speed v of the particle The magnitude and direction of depend on the velocity of the particle and on the magnitude and direction of the magnetic field (Tesla, T=N.s/(C.m), in SI unit) When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero
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Magnetic Fields and Forces
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Example #13 An electron in a television picture tube moves toward the front of the tube with a speed of 8.0 x10 6 m/s along the x axis (see the figure). Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 60 0 to the x axis and lying in the xy plane. Calculate the magnetic force on the electron.
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Magnetic Force Acting on a Current-Carrying Conductor The resultant force exerted by the field on the wire is the vector sum of the individual forces exerted on all the charged particles making up the current
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Magnetic Force Acting on a Current-Carrying Conductor
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n : the number of charges per unit volume
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Magnetic Force Acting on a Current-Carrying Conductor
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The magnetic force on a curved current- carrying wire in a uniform magnetic field is equal to that on a straight wire connecting the end points and carrying the same current
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Magnetic Force Acting on a Current-Carrying Conductor The net magnetic force acting on any closed current loop in a uniform magnetic field is zero
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Quiz#3 Rank the wires according to the magnitude of the magnetic force exerted on them, from greatest to least
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Sources of the Magnetic Field The Biot–Savart Law 0 : 4 x 10 -7 T.m/A
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Magnetic Field Surrounding a Thin, Straight Conductor
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Magnetic Field on the Axis of a Circular Current Loop At x=0 If x>>R
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Magnetic Field on the Axis of a Circular Current Loop
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The Magnetic Force Between Two Parallel Conductors Parallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in opposite directions repel each other
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Ampère’s Law
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The line integral of around any closed path equals 0 I, where I is the total steady current passing through any surface bounded by the closed path
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Quiz#4 Rank the magnitudes of for the closed paths in the figure from least to greatest
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The Magnetic Field of a Solenoid A solenoid is a long wire wound in the form of a helix
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The Magnetic Field of a Solenoid
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From Ampère’s Law N: the number of turns n: the number of turns per unit length
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Magnetic Flux
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Gauss’s Law in Magnetism The net magnetic flux through any closed surface is always zero
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The Magnetic Field of the Earth
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Faraday’s Law of Induction An electric current can be induced in a secondary circuit by a changing magnetic field An induced emf is produced in the secondary circuit by the changing magnetic field The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit
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Faraday’s Law of Induction a coil consisting of N loops all of the same area
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Faraday’s Law of Induction
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Lenz’s Law The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop
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Lenz’s Law
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