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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]
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that emf (electromagnetic work done on a unit charge when ...
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).
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units.
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 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.
where = is the distance of each charge from the test charge, which situated at the point , and () is the electric potential that would be at if the test charge were not present. If only two charges are present, the potential energy is Q 1 Q 2 / ( 4 π ε 0 r ) {\displaystyle Q_{1}Q_{2}/(4\pi \varepsilon _{0}r)} .