Advertisements
Advertisements
प्रश्न
Find the magnetic field due to a long straight conductor using Ampere’s circuital law.
Advertisements
उत्तर
Consider a straight conductor of infinite length carrying current I and the direction of magnetic field lines. Since the wire is geometrically cylindrical in shape C and symmetrical about its axis, we construct an Amperian loop in the form of a circular shape at a distance r from the centre of the conductor. From the Ampere’s law, we get
Ampèrian loop for current carrying straight wire
`oint_"C" vec"B"*"d"vec"l" = mu_0 "I"`
Where dl is the line element along the amperian loop (tangent to the circular loop). Hence, the angle between the magnetic field vector and line element is zero. Therefore,
`oint_"C" "B"*"dl" = mu_0 "I"`
where I is the current enclosed by the Amperian loop. Due to the symmetry, the magnitude of the magnetic field is uniform over the Amperian loop, we can take B out of the integration.
`"B"oint_"C" "dl" = mu_0"I"`
For a circular loop, the circumference is 2πr, which implies,
`"B"int_hat"n"^(2pi"r") "dl" = mu_0 "I"`
`vec"B"*2pi"r" = mmu_0"I"`
`=> vec"B" = (mu_0"I")/(2pi"r")`
In vector form, the magnetic field is
`vec"B" = (mu_0"I")/(2pi"r")hat"n"`
Where `hat"n"` is the unit vector along the tangent to the Amperian loop. This perfectly agrees with the result obtained from Biot-Savarf s law as given in equation
`vec"B" = (mu_0"I")/(2pi"a") hat"n"`
APPEARS IN
संबंधित प्रश्न
State Ampere’s circuital law.
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?
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 ?
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?
A thin but long, hollow, cylindrical tube of radius r carries i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube (b) outside the tube.
Calculate the magnetic field inside and outside of the long solenoid using Ampere’s circuital law
Two identical current carrying coaxial loops, carry current I in opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C, then which statement is correct?
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:
Using Ampere’s circuital law, obtain an expression for magnetic flux density ‘B’ at a point near an infinitely long and straight conductor, carrying a current I.
