Advertisements
Advertisements
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.
Advertisements
उत्तर
`ointvecB*vecdl = mu_0I_(enclosed)`
`(I_(enclosed))/(pia^2) = I/(pir^2)`
`I_(enclosed) = I r_2/a^2`
`vecB*vecdl = Bdl (because costheta = 1)`
`therefore ointBdl = mu_0Ir_2/a^2`
`Bointdl = mu_0Ir^2/a^2`
`B(2pir) = mu_0 Ir^2/a^2`
`B = (mu_0)/(2pi) I/a^2 r `
(ii) For r > a
From Ampere’s circuital law,
`ointvecB*vecdl = mu_0 l_(enclosed)`
`vecB*vecdl =Bdt cos theta`
`theta = 0`
`I_(enclosed) = I`
`oint Bdl = mu_0I`
`Bointdl = mu_0I`
`B(2pir) = mu_0I`
`B= (mu_0)/(2pi) I/r`
APPEARS IN
संबंधित 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.
A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
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?
In order to have a current in a long wire, it should be connected to a battery or some such device. Can we obtain the magnetic due to a straight, long wire by using Ampere's law without mentioning this other part of the circuit?
A solid wire of radius 10 cm carries a current of 5.0 A distributed uniformly over its cross section. Find the magnetic field B at a point at a distance (a) 2 cm (b) 10 cm and (c) 20 cm away from the axis. Sketch a graph B versus x for 0 < x < 20 cm.
Find the magnetic field due to a long straight conductor using Ampere’s circuital law.
Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C ______.
- `oint B.dl = +- 2μ_0I`
- the value of `oint B.dl` is independent of sense of C.
- there may be a point on C where B and dl are perpendicular.
- B vanishes everywhere on C.
When current flowing through a solenoid decreases from 5A to 0 in 20 milliseconds, an emf of 500V is induced in it.
- What is this phenomenon called?
- Calculate coefficient of self-inductance of the solenoid.
