Magnetics 2 Question 10

10. A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the XY plane and a steady current I flows through the wire. The Z-component of the magnetic field at the centre of the spiral is

(2011)

(a) μ0NI2(ba)lnba

(b) μ0NI2(ba)lnb+aba

(c) μ0NI2blnba

(d) μ0NI2blnb+aba

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Answer:

Correct Answer: 10. (a)

Solution:

  1. If we take a small strip of dr at distance r from centre, then number of turns in this strip would be,

dN=Nbadr

Magnetic field due to this element at the centre of the coil will be

dB=μ0(dN)I2r=μ0NI(ba)drrB=r=ar=bdB=μ0NI2(ba)lnba



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