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Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
From the simple one dimensional model = [() (+)] = = Expanding to 3 degrees of freedom = = The mean velocity due to the Electric field (given the equation of motion above at equilibrium) = To have a total current null + = we have = = And as usual in the Drude case = = = / where the typical thermopowers at room temperature are 100 times smaller ...
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, [1] one arrives at the three mathematical equations used to describe this relationship: [2]
The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v , with respect to a magnet is calculated in the frame of reference of the magnet and in the ...
Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing ...
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative ...
The current 3-form can be integrated over a 3-dimensional space-time region. The physical interpretation of this integral is the charge in that region if it is spacelike, or the amount of charge that flows through a surface in a certain amount of time if that region is a spacelike surface cross a timelike interval.
The telegrapher's equations then describe the relationship between the voltage V and the current I along the transmission line, each of which is a function of position x and time t: = (,) = (,) The equations themselves consist of a pair of coupled, first-order, partial differential equations. The first equation shows that the induced voltage is ...