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
A long straight wire of a circular cross-section of radius ‘a’ carries a steady current ‘I’. The current is uniformly distributed across the cross-section. Apply Ampere’s circuital law to calculate the magnetic field at a point ‘r’ in the region for (i) r < a and (ii) r > a.
A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The magnetic field
(a) increases linearly from the axis to the surface
(b) is constant inside the tube
(c) is zero at the axis
(d) is zero just outside the tube.
Consider the situation described in the previous problem. Suppose the current i enters the loop at the points A and leaves it at the point B. Find the magnetic field at the centre of the loop.
A thin but long, hollow, cylindrical tube of radius r carries i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube (b) outside the tube.
A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnitude filed at a point (a) just inside the tube (b) just outside the tube.
Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.
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.
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 ______.
The given figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a and r > a.
Briefly explain various ways to increase the strength of the magnetic field produced by a given solenoid.
