Advertisements
Advertisements
प्रश्न
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 ?
उत्तर
Solenoid
• It consists of an insulating long wire closely wound in the form of helix.
• Its length is large as compared to its diameter.
• Magnetic field due to RQ and SP path is zero because they are perpendicular to the axis of solenoid. Since SR is outside the solenoid, the magnetic field is zero.
• The line integral of magnetic field induction `vecB` over the closed path PQRS is
`oint_(PQRS) vecB*vecdl =oint_(PQ)vecB*vecdl =BL`
From Ampere’s circuital law,
`oint_(PQRS)vecB*vecdl = mu_0 `× Total current through rectangle PQRS
BL = μ0 × Number of turns in rectangle × Current
BL = μ0nLI
∴ B= μ0nI
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.
Obtain an expression for magnetic induction along the axis of the toroid.
Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.
Calculate the magnetic field inside and outside of the long solenoid using 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 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 ______.
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:
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:
Briefly explain various ways to increase the strength of the magnetic field produced by a given solenoid.
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.
