PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
Share
Notifications

View all notifications

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 - PUC Karnataka Science Class 12 - Physics

Login
Create free account


      Forgot password?

Question

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.

Solution

`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`

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [2]

Solution 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 Concept: Ampere’s Circuital Law.
S
View in app×