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The force initially results in an acceleration parallel to itself, but the magnetic field deflects the resulting motion in the drift direction. Once the particle is moving in the drift direction, the magnetic field deflects it back against the external force, so that the average acceleration in the direction of the force is zero.
A magnetic field is a vector field, but if it is expressed in Cartesian components X, Y, Z, each component is the derivative of the same scalar function called the magnetic potential. Analyses of the Earth's magnetic field use a modified version of the usual spherical harmonics that differ by a multiplicative factor.
The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force. [2]: ch1 The first is the electric field, which describes the force acting on a stationary charge and gives the component of the force that is independent of motion.
To simplify, let the magnetic field point in the z-direction and vary with location x, and let the conductor translate in the positive x-direction with velocity v. Consequently, in the magnet frame where the conductor is moving, the Lorentz force points in the negative y -direction, perpendicular to both the velocity, and the B -field.
A magnetic field in a coil of wire and the electric current in the wire. The force of a magnetic field on a charged particle, the magnetic field itself, and the velocity of the object. The vorticity at any point in the field of the flow of a fluid; The induced current from motion in a magnetic field (known as Fleming's right-hand rule).
The thumb shows the direction of motion and the index finger shows the field lines and the middle finger shows the direction of induced current. If an external magnetic field is applied horizontally, so that it crosses the flow of electrons (in the wire conductor, or in the electron beam), the two magnetic fields will interact.
The Lorentz force law states that a charge subject to an electric field feels a force along the direction of the field, and a charge moving through a magnetic field feels a force that is perpendicular both to the magnetic field and to its direction of motion.
As a simple example from the physics of magnetically confined plasmas, consider an axisymmetric system with circular, concentric magnetic flux surfaces of radius (a crude approximation to the magnetic field geometry in an early tokamak but topologically equivalent to any toroidal magnetic confinement system with nested flux surfaces) and denote the toroidal angle by and the poloidal angle by .