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## The Magnetic Field

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**The Magnetic Field**Chapter 30**Magnetic Forces**• Magnetic Force - A force present when an electric charge is in motion. • A moving charge is said to produce a magnetic field . • Magnetic fields exert forces on moving charges.**Magnetic Fields**• Represented by field lines . • By definition: • or more commonly: • Where q is the angle between v and B.**Magnetic Field Units**• Standard Unit = Tesla (T) • 1 T = 1 N/A•m • 1 T = 104 gauss**Force on Moving Charges**• The diagram below shows a uniform magnetic field with several charges in motion. v v v v**Force on Moving Charges**• The magnitude of the force on each charge can be found by qvXB or qvBsinq. • The direction of the force is found by a right hand rule.**Right Hand Rule**• 1) Place your fingers in the direction of the velocity. • 2) Curl your fingers toward the direction of the field. You might need to turn your hand. • 3) Your thumb points in the direction of the force.**Direction of Force**v F F = 0 v F F v v**Magnetic Field Lines**• NOT lines of force. • Force on charges is not in the direction of the magnetic field. • Force is always perpendicular to the velocity of the charge. • Force is always perpendicular to the magnetic field. • RHR & LHR**Permanent Magnets**• Magnetic field lines point away from north poles • and toward south poles.**Magnetic Flux**• The amount of a magnetic field passing through a given area. • Proportional to the number of magnetic field lines which pass through an area.**Magnetic Flux**Maximum Flux A A A No Flux**Flux Units**• Weber • 1 Wb = 1 T/m2**Gauss's Law for Magnetism**• The magnetic flux through any closed surface must be zero. N S**Example**• Exercise 4**homework**• E 1, 2, 7**Motion of Charges in a Magnetic Field**• Two possible paths can result for the motion of the charge: • 1) If vo is perpendicular to B, a circular path will result. • 2) If vo is not perpendicular to B, the charge will travel in a spiral path.**Motion of Charges**• As a charge circles or spirals in a magnetic field, the radius of its path is dependent on the perpendicular component of its velocity.**Velocity Selector**• Only allows charges with a specific velocity to pass through undeflected. • FB is opposite of FE • E is perpendicular to B**Velocity Selector**FE FB**Velocity Selector**• For a specific value of v, the electric force and the magnetic force will be equal to each other and opposite in direction. • FB = FE • qvB = qE • vB = E**Current-Carrying Wire**• Since a current is moving charges, a current-carrying wire experiences a force in a magnetic field. (B into screen) F X X X X X X X X X X X X X X X X**Example**• Exercise 14**homework**• E 19, 20**Sources of Magnetic Fields**Chapter 31**Long, straight wire**mo is equal to 4p x 10–7 T•m/A.**Current Carrying Wire**• Shape of the field is circular. • Concentric circles • The direction is given a Right Hand Rule: • Thumb in the direction of the current. • Curl your fingers and they give the direction of the field.**Moving Charge**+ • v**I**B Wire • • • • • • • • • I x x x x x x x x x**Parallel conductors**• Each creates a magnetic field that produces a force on the other • Can calculate force per unit length • To find direction, use both right hand rules**Definition of Ampere**• Comes from force exerted by two parallel conductors • 1 A is the current necessary in each conductor (if 1 m apart) to produce a force of 2 x 10-7 N.**Field of a circular loop or coil**• At center of loop • Direction found with right hand rule – like current in straight wire**Field of a Solenoid**• Long Spring-like Coil • Uniform field in the interior:**Examples**• Exercises 1 and 7**homework**• E 2, 6, 10, 12**Ampere’s Law**• Like Gauss’s law I**Example**• A wire has a radius of R and carries a current I that is uniformly distributed across its area. • Determine how to calculate the magnitude of the magnetic field inside and outside the conductor.**R**r Inside • The current inside a circle of radius r would be a fraction of the total current. • Same ratio as areas. • With total current, I:**Outside**• A circle of radius r, where r > R, encloses all the current. r R**Example**• Determine the field inside a solenoid**Solenoid**• Vertical sides – zero because B is perpendicular to sides • Side outside solenoid – if it is far away from the solenoid, B is zero**Paramagnetic materials**• Can become magnetized • An external magnetic field causes atoms to line up so their currents add to the external field**Ferromagnetic materials**• Atomic currents line up even when no external field is present • Permanent magnets