Advertisements
Advertisements
प्रश्न
Write Maxwell's generalization of Ampere's circuital law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is `I=varepsilon_0 (dphi_E)/dt,`where ΦE is the electric flux produced during charging of the capacitor plates.
Advertisements
उत्तर
A moving charge produces both electric and magnetic fields, and an oscillating charge produces oscillating magnetic and electric fields. These oscillating electric and magnetic fields with respect to space and time produce electromagnetic waves.
The propagation of electromagnetic waves can be shown as
OR
Maxwell's generalisation of Ampere's circuital law is given as follows:
`oint vec"B".vec"dl"=mu_0(I+I_D)=mu_0(I+varepsilon_0 (dphi)/dt)`
Consider that a parallel capacitor C is charging in a circuit.
The magnitude of electric field between the two plates will be `E=q/(varepsilon_0 A)`and is perpendicular to the surface of the plate.
`phi_E=vecE.vecA=EA cos0=q/(varepsilon_0 A)xxA=q/varepsilon_0`
`=>(dphi_E)/dt=(d(q/varepsilon_0))/dt`
`=>(dq)/dt=varepsilon_0(dphi_E)/dt ("Here, dq/dt is rate of change of charge with time.")`
`=>I=varepsilon_0(dphi_E)/dt`
APPEARS IN
संबंधित प्रश्न
State Ampere’s circuital law.
Obtain an expression for magnetic induction along the axis of the toroid.
Explain Ampere’s circuital law.
In Ampere's \[\oint \vec{B} \cdot d \vec{l} = \mu_0 i,\] the current outside the curve is not included on the right hand side. Does it mean that the magnetic field B calculated by using Ampere's law, gives the contribution of only the currents crossing the area bounded by the curve?
Consider the situation of the previous problem. A particle having charge q and mass mis projected from the point Q in a direction going into the plane of the diagram. It is found to describe a circle of radius r between the two plates. Find the speed of the charged particle.
Using Ampere's circuital law, obtain an expression for the magnetic flux density 'B' at a point 'X' at a perpendicular distance 'r' from a long current-carrying conductor.
(Statement of the law is not required).
State Ampere’s circuital law.
A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by another wire of 1 mm diameter carrying the same current. The strength of the magnetic field far away is ______.
