Advertisements
Advertisements
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.
Advertisements
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`
APPEARS IN
RELATED QUESTIONS
Explain Ampere’s circuital law.
Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis ?
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?
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.
What is magnetic permeability?
State Ampere’s circuital law.
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 long solenoid having 200 turns per cm carries a current of 1.5 amp. At the centre of it is placed a coil of 100 turns of cross-sectional area 3.14 × 10−4 m2 having its axis parallel to the field produced by the solenoid. When the direction of current in the solenoid is reversed within 0.05 sec, the induced e.m.f. in the coil is:
Ampere's circuital law is used to find out ______
