  # Magnetism The right-hand rule gives the direction of a vector resulting from the cross product of two other vectors. To find the direction of the resulting vector sweep the fingers of the right hand from the direction of the first vector to the direction of the second vector over the smallest possible angle between the vectors. The direction in which the thumb points is the direction of the resulting vector.

 Q:    If a charged particle moves in a straight line with constant speed through some region in space, is the magnetic field in that region zero? A:    Maybe, maybe not.  The only true conclusion we can draw is that the particle has no force applied on it.  This can happen when either there is no magnetic field, or when there is a field oriented in a direction parallel to the velocity of the particle.  Remember that the formula for the force applied by a magnetic field on a moving charge is F = q ( v x B ).  The magnitude of this force is F = q v B ( sin ), where is the angle between velocity v and magnetic field B.   So, if v is parallel to B, sin is zero and therefore the force F is zero. Q:    In some science fiction cartoons, books, and movies, force fields are used to contain things such as people, contaminated substances, etc..  Are these types of fields scientifically grounded? A:    Oh, yes!   Material bodies consist of atoms which, in their turn, consist of charged particles (protons and electrons).  Such charged particles can be confined within restricted regions in space by magnetic fields.  So, confinement is possible; the problem is that the charged particles should be moving in directions perpendicular to the magnetic field.  Then they would move in circles around the lines of magnetic field.  In science fiction, everything is possible.  In the real world, magnetic confinement has been achieved for charged particles moving at tremendous speeds (corresponding to energies similar to those in the sun) in a magnetic field device called a torus.   Superconducting magnets (electromagnets fed by very large steady currents passing through superconducting wires, kept at very low temperatures - close to absolute zero) in the shape of donuts, create circular magnetic field lines around which the fast charged particles execute circular or spiral trajectories.  This type of magnetic device is called TOKAMAK.  There is a hope that in installation of this type, fusion energy can be generated to satisfy the needs of the world.  In a fusion process, two very fast protons (nuclei of the hydrogen atom) would collide with each other and merge to form a helium nucleus and emit the desired energy.  Hydrogen would be provided with cheap means from the almost unlimited amount of ocean water.  Fusion research has been funded in the last fifty years and yet no fusion energy is available at a large scale.   It is believed that it will take at least fifty more years until fusion will solve the world's energy problems.  One more comment: very energetic particles are said to be hot; so we talk about the particles in the TOKAMAK as being at temperature of hundreds of millions of degrees.  No solid containers made out of materials known to man are capable to withstand such temperatures.  Only "no wall" magnetic confinement TOKAMAKs can achieve this purpose.  Now you see why magnetic confinement of living bodies are possible only in science fiction cartoons, books, and movies, and in our imagination.

## References

### Facts

The SI unit for magnetic field (B) is the tesla (T), 1 T = 1 N/(A . m) = 104 gauss

### Equations

Magnetic field (B)

FB = q v B

Magnitude of the force on a particle in a magnetic field.

FB = | q | v B sin The Hall Effect, number density of charge carriers on a conducting strip in a magnetic field A charge particle circulating in a magnetic field

 From Newton's Second Law Radius of Circle Frequency of revolution, angular frequency, and period Magnetic force on a current-carrying wire

FB = i L B

Magnetic force acting on a current element ( i dL) in a magnetic field

dFB = i dL B

Torque on a current-carrying coil Magnetic potential energy of a magnetic dipole # List of Topics

 Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  ครั้งที่

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