Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Magnetism question

2011 · Shift 2 · Q51
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Advanced
  3. /Physics
  4. /Magnetism
  5. /2011 · Shift 2 · Q51

Magnetism question

2011 · Shift 2 · Q51

JEE AdvancedPhysicsMagnetismMCQ+3 / −1
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 IIT-JEE 2011 Paper 2 Offline Physics - Magnetism Question 16 English
  1. A
    μ0NI2(b−a)ln⁡(ba){{{\mu _0}NI} \over {2(b - a)}}\ln \left( {{b \over a}} \right)2(b−a)μ0​NI​ln(ab​)
  2. B
    μ0NI2(b−a)ln⁡(b+ab−a){{{\mu _0}NI} \over {2(b - a)}}\ln \left( {{{b + a} \over {b - a}}} \right)2(b−a)μ0​NI​ln(b−ab+a​)
  3. C
    μ0NI2bln⁡(ba){{{\mu _0}NI} \over {2b}}\ln \left( {{b \over a}} \right)2bμ0​NI​ln(ab​)
  4. D
    μ0NI2bln⁡(b+ab−a){{{\mu _0}NI} \over {2b}}\ln \left( {{{b + a} \over {b - a}}} \right)2bμ0​NI​ln(b−ab+a​)
View written solutionFree

Correct answer: A

  1. Model the spiral as many circular turns

Since the wire is closely wound from inner radius aaa to outer radius bbb with total number of turns NNN, we can treat it as a continuous distribution of concentric circular loops.

If dNdNdN turns lie in a radial thickness drdrdr, then because the winding is uniform,

dNdr=Nb−a\frac{dN}{dr} = \frac{N}{b-a}drdN​=b−aN​

so,

dN=Nb−a drdN = \frac{N}{b-a}\,drdN=b−aN​dr
  1. Magnetic field at the centre due to one circular turn

For a circular loop of radius rrr carrying current III, the magnetic field at its centre is

dBz=μ0I2rdB_z = \frac{\mu_0 I}{2r}dBz​=2rμ0​I​

Since all turns lie in the xyxyxy-plane and current flows in the same sense, all contributions are along the same zzz-direction.

Including dNdNdN turns in the shell between rrr and r+drr+drr+dr,

dBz=μ0I2r dNdB_z = \frac{\mu_0 I}{2r}\, dNdBz​=2rμ0​I​dN

Substitute dNdNdN:

dBz=μ0I2r⋅Nb−a drdB_z = \frac{\mu_0 I}{2r}\cdot \frac{N}{b-a}\,drdBz​=2rμ0​I​⋅b−aN​dr
  1. Integrate from inner radius aaa to outer radius bbb
Bz=∫abdBz=∫abμ0IN2(b−a)drrB_z = \int_a^b dB_z = \int_a^b \frac{\mu_0 I N}{2(b-a)}\frac{dr}{r}Bz​=∫ab​dBz​=∫ab​2(b−a)μ0​IN​rdr​ Bz=μ0IN2(b−a)∫abdrrB_z = \frac{\mu_0 I N}{2(b-a)} \int_a^b \frac{dr}{r}Bz​=2(b−a)μ0​IN​∫ab​rdr​ Bz=μ0IN2(b−a)ln⁡(ba)B_z = \frac{\mu_0 I N}{2(b-a)} \ln\left(\frac{b}{a}\right)Bz​=2(b−a)μ0​IN​ln(ab​)
  1. Match with options

Thus,

Bz=μ0NI2(b−a)ln⁡(ba)B_z = \frac{\mu_0 N I}{2(b-a)}\ln\left(\frac{b}{a}\right)Bz​=2(b−a)μ0​NI​ln(ab​)

This matches Option A.

  1. Check against stored answer

Stored correct answer: A

Derived answer: A

They agree.

PreviousNext

More from Magnetism

  • A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of… Includes diagram2010 · MCQ
  • Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that… Includes diagram2010 · MCQ
  • Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that… Includes diagram2010 · MCQ
  • A steady current I goes through a wire loop PQR having shape of a right angle triangle wit6h PQ = 3, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k(48πxμ0​I​),…2009 · Numerical
  • A particle of mass m and charge q, moving with velocity v enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is l.… Includes diagram2008 · Multiple correct
  • STATEMENT 1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. and STATEMENT 2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or…2008 · MCQ
  • A magnetic field B=B0​j^​ exists in the region a<x<2a and B=−B0​j^​, in the region 2a<x<3a, where B0​ is a… Includes diagram2007 · MCQ
  • Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer… Includes table Includes diagram2007 · MCQ