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
Maxwell's generalisation of Ampere's circuital law is given as follows:
`ointvecB.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
Electron drift speed is estimated to be of the order of mm s−1. Yet large current of the order of few amperes can be set up in the wire. Explain briefly.
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.
Define ampere.
The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
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 ______.
Ampere’s circuital law is given by _______.
Briefly explain various ways to increase the strength of the magnetic field produced by a given solenoid.
