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But when the inducing charge is moved away, the charge is released and spreads throughout the electroscope terminal to the leaves, so the gold leaves move apart again. The sign of the charge left on the electroscope after grounding is always opposite in sign to the external inducing charge. [5] The two rules of induction are: [5] [6]
Maxwell's equations describing the Faraday's and Ampere's laws read: =, and =, where: is the electric field. is the magnetic field. is the vacuum permeability.; is the electric current density.
The induced B-field increases the flux on this side of the circuit, opposing the decrease in flux due to r the rotation. The energy required to keep the disc moving, despite this reactive force, is exactly equal to the electrical energy generated (plus energy wasted due to friction , Joule heating , and other inefficiencies).
The result (proved below) is that the total charge induced on the inside of the container is equal to the charge on C. In Procedure 5, when C is touched to the container's inner wall, all the charge on C flows out and neutralizes the induced charge, leaving both the inner wall and C uncharged. The container is left with the charge on its outside.
Contact-induced charge separation causes one's hair to stand up and causes "static cling" (for example, a balloon rubbed against the hair becomes negatively charged; when near a wall, the charged balloon is attracted to positively charged particles in the wall, and can "cling" to it, suspended against gravity).
where n is the number of charges, q i is the amount of charge associated with the ith charge, r i is the position of the ith charge, r is the position where the electric field is being determined, and ε 0 is the electric constant. If the field is instead produced by a continuous distribution of charge, the summation becomes an integral:
The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: = [′ ′ + ′ (′ ′) + ′] = ′ Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light.
The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion. Lenz's law is contained in the rigorous treatment of Faraday's law of induction (the magnitude of EMF induced in a coil is proportional to the rate of change of the magnetic flux ...