Advertisements
Advertisements
प्रश्न
A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of the magnitude of magnetic field `vecB_1` at `a/2` and `vecB_2` at distance 2a is ______.
विकल्प
`1/2`
1
2
4
Advertisements
उत्तर
A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of the magnitude of magnetic field `vecB_1` at `a/2` and `vecB_2` at distance 2a is 1.
Explanation:
Consider two amperian loops of radius `a/2` and 2a. Applying Ampere's circuital law for these loops.
We get `ointB.dL = μ_0I_{"enclosed"}`
For the smaller loop,
`B_1 xx 2pi a/2 = mu_0 xx pia^2 1 xx (a/2)^2`
`mu_0I xx 1/4 = (mu_0I)/4`
`B_1 = (mu_0I)/(4pia)`
`B_2 xx 2pi(2a) = mu_0I`
`B_2 = (mu_0I)/(4pia)`
∴ B1/B2 = `(mu_0I)/(4pia) xx (4pia)/(mu_0I) = 1`
संबंधित प्रश्न
State Ampere’s circuital law.
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.
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 long, straight wire carries a current. Is Ampere's law valid for a loop that does not enclose the wire, or that encloses the wire but is not circular?
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.
Using Ampere's circuital law, obtain an expression for the magnetic flux density 'B' at a point 'X' at a perpendicular distance 'r' from a long current-carrying conductor.
(Statement of the law is not required).
What is magnetic permeability?
Ampere’s circuital law is given by _______.
In a capillary tube, the water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the radius of the first is:
A solenoid of length 0.6 m has a radius of 2 cm and is made up of 600 turns If it carries a current of 4 A, then the magnitude of the magnetic field inside the solenoid is:
