Subjective Type

Calculate the magnetic moment of a thin wire with a current $$I = 0.8\ A$$, wound tightly on half a tore (Fig.). The diameter of the cross-section of the tore is equal to $$d = 5.0\ cm$$, the number of turns is $$N = 500$$.

Solution

Take an element of length $$rd\theta$$ containing $$\displaystyle\frac{N}{\pi r}\cdot rd\theta$$ turns. Its magnetic moment is

$$\displaystyle\frac{N}{\pi}d\theta\cdot\frac{\pi}{4}d^2I$$

normal to the plane of cross section. We resolve it along $$OA$$ and $$OB$$. The moment along $$OA$$ integrates to

$$\displaystyle\int_0^{\displaystyle\pi}{\frac{N}{4}d^2Id\theta\cos{\theta}}=0$$

while that along $$OB$$ gives

$$\displaystyle p_m=\int_0^{\displaystyle\pi}{\frac{Nd^2I}{4}}\sin{\theta}d\theta=\frac{1}{2}Nd^2I$$

SIMILAR QUESTIONS

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A toroid with mean radius $${ r }_{ 0 }$$ and diameter $$2a$$ has N turns carrying current I. What is the magnetic field B inside the toroid?

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For a toroid $$N = 500, radius = 40\ cm$$, and area of cross section $$= 10 cm^{2}$$. Find inductance.

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A toroid has a core (non -ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.

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Magnetism

Fig. shows a torodial solenoid whose cross-section is rectangular. Find the magnetic flux through this cross-section if the current through the winding equals $$I = 1.7\ A$$, the total number of turns is $$N = 1000$$, the ratio of the outside diameter to the inside one is $$\eta = 1.6$$, and the height is equal to $$h = 5.0\ cm$$.

Magnetism

A Rowland ring is formed of ferromagnetic material. It is circular in cross-section, with an inner radius of $$5.0$$ cm and an outer radius of $$6.0$$ cm, and is wound with $$400$$ turns of wire. (a) What current must be set up in the windings to attain a toroidal field of magnitude $$B_0 = 0.20$$ mT? (b) A secondary coil wound around the toroid has $$50$$ turns and resistance $$8.0\,\Omega$$. If, for this value of $$B_0$$, we have $$B_M = 800B_0$$, how much charge moves through the secondary coil when the current in the toroid windings is turned on?

Magnetism

A toroid having a square cross section, 5.00 cm on a side, and an inner radius of 15.0 cm has 500 turns and carries a current of 0.800A.What is the magnetic field inside the toroid at (a) the inner radius and (b) the outer radius?

Magnetism

A solenoid is 1.5$$m$$ long and its inner diameter is 4.0$$ { cm }$$ . It has 3 layers of winding's of 1000 turns each and carries a current of 2.0 amperes.The magnetic flux for a cross-section of the solenoid is nearly.

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