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Download Lecture 8 Magnetic field
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Magnetic Poles Every magnet, regardless of its shape, has two poles Called north and south poles Poles exert forces on one another Similar to the way electric charges exert forces on each other Same poles repel each other ; opposite poles attract each other The force between two poles varies as the inverse square of the distance between them Magnetic poles are always found in pairs Magnetic Field The region of space surrounding any moving electric charge also contains a magnetic field A magnetic field also surrounds a magnetic substance making up a permanent magnet A vector quantity Symbol : B Direction is given by the direction a north pole of a compass needle points in that location Magnetic Force The magnetic field can be defined in terms of magnetic force The magnetic force FB qv B FB q v B is the magnetic force is the charge is the velocity of the moving charge is the magnetic field Differences between E and B fields Direction of force Direction of FE is along E , while direction of FB is perpendicular to B. Motion FE acts on a charged particle regardless of whether the particle is moving, while FB acts only on a moving charged particle. Work FE produces work when acting on a charged particle, while FB produces no work when acting on a charged particle. Units of Magnetic Field The SI unit of magnetic field is the tesla (T) Wb N N T 2 m C ( m / s ) A m Wb is a weber A non-SI commonly used unit is a gauss (G) 1 T = 104 G Notation of Direction When vectors are perpendicular to the page, dots and crosses are used The dots represent the arrows coming out of the page The crosses represent the arrows going into the page Charged Particle in a Magnetic Field Consider a particle moving in an external magnetic field with its velocity perpendicular to the field The force is always directed toward the center of the circular path mv 2 FB qvB r mv r qB More About Motion of Charged Particle The angular speed of the particle is v qB ω r m The angular speed, w, is also referred to as the cyclotron frequency The period of the motion is 2πr 2π 2πm T v ω qB Charged Particles Moving in Electric and Magnetic Fields In that case, the total force is the sum of the forces due to the individual fields In general: F qE qv B Thomson’s e/m Experiment Magnetic Force on a Current Carrying Conductor A force is exerted on a current-carrying wire placed in a magnetic field The current is a collection of many charged particles in motion The direction of the force is given by the right-hand rule Force on a Wire, equation The magnetic force is exerted on each moving charge in the wire F qv B d The total force is the product of the force on one charge and the number of charges F qvd B nAL FB IL B Torque on a Current Loop The rectangular loop carries a current I in a uniform magnetic field No magnetic force acts on sides 1 & 3 Force on sides 2 & 4 : F2 = F4 = I a B The area enclosed by the loop is ab, so τmax = IAB Torque on a Current Loop, General IA B where A is perpendicular to the plane of the loop and has a magnitude equal to the area of the loop Magnetic Dipole Moment The product IA is defined as the magnetic dipole moment, , of the loop Often called the magnetic moment SI units: A · m2 Torque in terms of magnetic moment: B Analogous to p E for electric dipole Potential Energy The potential energy of the system of a magnetic dipole in a magnetic field depends on the orientation of the dipole in the magnetic field: U B Umin = -B and occurs when the dipole moment is in the same direction as the field Umax = +B and occurs when the dipole moment is in the direction opposite the field