Home
Class 12
PHYSICS
Calculate the magnetic moment (in Am^(2)...

Calculate the magnetic moment (in `Am^(2)` ) of a thin wire with a current I = 8A, wound tightly on half a torus (see figure). The diameter of the cross section of the torus is equal to d = 5 cm, and the number of turns is N = 500.

Text Solution

Verified by Experts

The correct Answer is:
`1/2 A.m^(2)`
`M=underset(theta=0)overset(pi)intdMsintheta`
`=underset(theta=0)overset(pi)int (dN) .i.A. sintheta =underset(0)overset(pi)int N/pi _|_ ((pd^(2))/4) sin theta d theta `
`M=1/2N.i.d^(2) rArr M=1/2(Amp m^(2))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTRODYNAMICS

    RESONANCE ENGLISH|Exercise Exercise-3 PART-3|29 Videos

  • ELECTRO MAGNETIC WAVES

    RESONANCE ENGLISH|Exercise Exercise 3|27 Videos

  • ELECTROMAGNETIC INDUCTION

    RESONANCE ENGLISH|Exercise A.l.P|19 Videos

Similar Questions

Explore conceptually related problems

Calculating the magnetic moment ( in Am^2 ) of a thin wire with a current I=8A, wound tightlly on a half a tore (see figure). The diameter of the cross section of the tore is equal to d=5cm, and the number of turns is N=500.

Calculating the magnetic moment ( in Am^2 ) of a thin wire with a current I=0.8A, wound tightlly on a half a tore (see figure). The diameter of the cross section of the tore is equal to d=5cm, and the number of turns is N=500.

Knowledge Check

  • A long straight cable of length l is placed symmetrically along z-axis and has radius a(ltlt l). The cable consists of a thin wire and a co- axial conducting tube. An alternating current I(t) = I_(0) " sin " (2pi vt) . Flows down the central thin wire and returns along the co-axial conducting tube. the induced electric at a distance s from the wire inside the cable is E(s ,t) =mu_(0) I_(0) v " cos "(2pivt) In ((s)/(a)) hatk . (i) Calculate the displacement current density inside the cable. (ii) Integrate the displacement current density across the cross- section of the cable to find the total displacement current I^(d) . (iii) compare the conduction current I_(0) with the displacement current I_(0)^(d) .

    A
    `(2pi)/(lamda^(2))I_(0)ln((a)/(s))sin(2pi upsilont)hat(k)`
    B
    `(1)/(lamda^(2))I_(0)ln((a)/(s))sin(2pi upsilont)hat(k)`
    C
    `(pi)/(lamda^(2))I_(0)ln((a)/(s))sin(2pi upsilon t)hat(k)`
    D
    Zero

  • A closely wound solenoid of 750 turns and area of cross section of 5xx 10^(4)m^(2) carries a current of 3.0 A. Its associated magnetic moment is

    A
    `4.12JT^(-1)`
    B
    `3.12JT^(-1)`
    C
    `2.12JT^(-1)`
    D
    `1.13JT^(-1)`

    • Similar Questions

    Explore conceptually related problems

    A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm^2 , the number of turns is N = 60 . When the coil turns through 180^@ about its diameter, a galvanometer connected to the coil indicates a charge q = 4.5muC flowing through it. Find the magnetic induction magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 Omega .

    Find the magnetic induction of the field at the point O at a loop with current I , whose shape is illustrated in figure (a)In figure a the radii a and b , as well as the angle varphi are known (b)In figure b ,the raidus a and the side b are known. (c)A current I=5.0 A flows along a thin wire shaped as shown in figure.The radius of a curved part of the wire is equal to R=120 mm ,the angle 2varphi=90^(@) .Find the magnetic induction of the field at the point O .

    A plane spiral with a great number N of turns wound tightly to one another is located in a uniform magnetic field perpendicular to the spiral's plane.The outside radius of the spiral's turns is equal to a and inner radius is zero.The magnetic induction varies with time as B=B_(0) sin omega t , where B_(0) and omega are constants.The amplitude of emf induced in the spiral is epsilon_(im)=1/xpia^(2) NomegaB_(0) .Find out value of x .

    (a) Calculate the self-inductance of a solenoid that is tightly wound with wire of diameter 0.10 cm , has a cross-sectional area 0.90 cm^2 and is 40 cm long (b) If the current through the solenoid decreases uniformly from 10 A to 0 A in 0.10 s , what is the emf induced between the ends of the solenoid?

    Calculate the drift speed of the electrons when 1A of current exists in a copper wire of cross section 2 mm^(2) .The number of free electrons in 1cm^(3) of copper is 8.5xx10^(22) .

    A thin wire is wound very tightly in one layer on the surface of a sphere of paramagnetic material (mu_(r)~~1) . The planes of all the turns can be assumed to be perpendicular to the same diameter of the sphere. The turns over the entire surface of the sphere. The radius of the sphere is R , the total number of turns is N , and the current in the winding is I . Find the magnetic induction at the centre of the sphere. (Given mu_(0)NI=20R )

    Home
    Profile