Advertisements
Advertisements
प्रश्न
Obtain an expression for magnetic induction of a toroid of ‘N’ turns about an axis passing through its centre and perpendicular to its plane.
उत्तर
The toroid is a solenoid bent into the shape of a hollow doughnut.
According to Ampere's circuital law.
`phivecB.vec(dL) = mu_0I`
Here current 'I' flow through the ring as many times as there are the N no. of turns.
∴ `phivecB.vec(dL) = mu_0NI` ..........(1)
Now, B and dL are in the same direction.
∴ `phivecB.vec(dL) = BphidL`
∴ `phivecB.vec(dL) = B.(2pir)` .....(2)
From (1) and (2),
`mu_0NI = B.(2pir)`
∴ B = `(mu_0NI)/(2pir)`
APPEARS IN
संबंधित प्रश्न
A toroid of a central radius of 10 cm has windings of 1000 turns. For a magnetic field of 5 × 10-2 T along its central axis, what current is required to be passed through its windings?
What is Toroid?
A solenoid of length 50 cm of the inner radius of 1 cm and is made up of 500 turns of copper wire for a current of 5 A in it. What will be the magnitude of the magnetic field inside the solenoid?
Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid Why?
A solenoid of length π m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at its centre along the radius.
The length of solenoid is I whose windings are made of material of density D and resistivity p. The winding resistance is R. The inductance of solenoid is
[m = mass of winding wire, µ0 = permeability of free space]
A winding wire which is used to frame a solenoid can bear a maximum of 20 A current. If the length of the solenoid is 80 cm and its cross-sectional radius is 3 cm, then the required length of winding wire is ______ (B = 0.2 T)
Two current-carrying coils have radii r and 4r and have same magnetic induction at their centres. The ratio of voltage applied across them is ______.
Two toroids 1 and 2 have total number of turns 400 and 200 respectively with average radii 40 cm and 20 cm respectively. If they carry same current I, the ratio of the magnetic fields along the two loops is, ____________.
A proton is projected with a uniform velocity 'v' along the axis of a current carrying solenoid, then ____________.
The space within a current carrying toroid is filled with a m metal of susceptibility 16.5 x 10-6. The percentage increase in the magnetic field B is ____________.
Magnetic induction due to a toroid does not depend upon ______.
A toroid is a long coil of wire wound over a circular core. If 'r' and 'R' are the radii of the coil and toroid respectively, the coefficient of self-induction of the toroid is (The magnetic field in it is uniform and R > > r) ____________.
(N = number of turns of the coil and µ0 = permeability of free space)
The magnetic flux near the axis and inside the air core solenoid of length 60 cm carrying current 'I' is 1.57 × 10-6 Wb. Its magnetic moment will be ______.
(cross-sectional area is very small as compared to length of solenoid, µ0 = 4π × 10-7 SI unit)
A long solenoid carrying current 'I1' produces magnetic field 'B1' along its axis. If the current is reduced to 25% and number of turns per cm are increased four times, then new magnetic field 'B2' is ____________.
A winding wire is used to prepare a solenoid that can bear a maximum current of 10A. If the length of a solenoid is 80 cm and its cross-sectional radius is 3 cm, the required length of winding wire is ____________.
(magnetic field B = 0.2 T, µ0 = 4 x 10-7 SI units)
A toroid has a core of inner radius 20 cm and outer radius 22 cm around which 4200 turns of a wire are wound. If the current in the wire is 10 A. What is the magnetic field inside the core of toroid?
In a current-carrying long solenoid, the field produced does not depend upon ______
A straight solenoid has 50 turns per cm in primary and 200 turns per cm in the secondary. The area of cross-section of the solenoid is 4 cm2. The mutual inductance is ______.
A conducting rod along the equator is 1 m long and carries a current of 15 A from east to west. The magnitude of Earth's magnetic field at the equator is `4/3 xx 10^(-4)` T. The magnitude and direction of the force on the rod are ______.
For a solenoid and a toroid, the number of turns per unit length is n and the respective interior volume is V. The self inductance is proportional to n2 and V for ______.
A current of 10 A passes through a coil having 5 turns and produces magnetic field at the centre of the coil having magnitude 0.5 x 10-4 T. Calculate diameter of the coil.
(µ0 = 4π x 10-7 Wb/Am)
