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magnetic interaction

. +. +. v. B. F. magnetic interaction.

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magnetic interaction

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  1. + + v B F magnetic interaction There is interaction between a particle and other bodies which depends on the charge of the particle, its position and its velocity (and its spin). We call this interaction a magnetic interaction. Moving charged particles in the body cause the magnetic interaction. The region of space in which magnetic forces can be exerted is called a magnetic field. O

  2. The magnetic field vector at position is a vector such that, at this position, the magnetic force exerted on a particle with charge q, moving with velocity , would be + + B F v magnetic field vector

  3. O  + + v B F the cyclotron frequency Recall that in a uniform circular motion: In a uniform magnetic field, the particle moves with constant angular velocity along the magnetic field

  4. + ds v B F work due to magnetic interaction The magnetic work performed on the particle is zero. (A magnetic field cannot change the speed of a particle.)

  5. The (differential) force , exerted on a (differential) segment, depends on the current I in the wire, the size ds and orientation of the segment, and the magnetic field vector at the location of the segment: B Ids dF magnetic force "on a current" I

  6. The magnetic moment of an object is a vector such that the magnetic torque exerted on the object (about its center of the mass) placed in the magnetic field is B B B B N S magnetic moment Puzzle. What is the direction of the magnetic moment of a compass needle?

  7. b a r t The magnetic moment of a wire loop carrying current depends on the current I in the loop and the area A of the loop.  magnetic moment of a current loop

  8. The potential energy of an object in a magnetic field depends on the magnetic moment of the object and the magnetic field at its location N S N S potential energy

  9. When the particle moves in the presence of both a magnetic field and an electric field, the net force depends on both fields: + V I + _ _ + _ + + _ _ + _ + _ + d The Lorentz force Example. The Hall effect FB vd FE

  10. Maxwell's equations . . . and God said: Let . . . . . . and there was light.

  11. The net electric flux through any closed (Gaussian) surface is proportional to the net charge inside the surface: The net magnetic flux through any closed (Gaussian) surface is equal to zero: N N Gauss‘s law for magnetic fields

  12. The line integral of the electric field vector around any closed path equals the rate of change in the magnetic flux through any surface bounded by that path. N E Faraday's law of induction B

  13. The circulation of the magnetic field vector around any amperian loop proportional the sum of the total conduction current and the displacement current through any surface bounded by that path. E B Ampere-Maxwell law I E The proportionality coefficient is called the permeability of free space.

  14. The rate of change in the electric field multiplied by the permittivity of free space is called the displacement current I I E displacement current Example: Q -Q

  15. v B + ds F Example: Magnetic field of a long straight wire with current I R

  16. dB r The (differential) magnetic field at a certain position P produced by a differential element carrying electric current I depends on the value of the current and the size and orientation of the segment. Ids the Biot-Savart law P I

  17. z y x dB r R Ids s  Example: infinite straight wire with current I P  -

  18. B1 The magnitude of the magnetic force exerted on segment l of a wire by the other wire (infinite) is F21 a Interaction between two parallel current I1 I2 l 2 1 Parallel "currents" attract and antiparallel repel.

  19. N S L magnetic field of a solenoid The magnetic field outside the solenoid is zero Bout 0 I The magnetic field inside is uniform, its direction is parallel to the axis, and the magnitude depends on the current and the number of loops per length of the solenoid Bin0nI I

  20. Bm B0 Magnetic properties of matter When a substance is placed in a (external) magnetic field, its molecules acquire a magnetic moment related to the external field. This creates an additional magnetic field (internal). paramagnetics:  > 1 diamagnetics:  < 1

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