The  ratio of magnetic fields on the axis of a circular

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 Multiple Choice QuestionsMultiple Choice Questions

241.

What is the dimensions of a magnetic field B in terms of C ( = coulomb ), M, L, T?

  • [ M1 L-1 T-2 C ]

  • [ M1 L0 T-1 C-1 ]

  • [ M1 L0 T-2 C ]

  • [ M1 L0 T-1 C ]


242.

Magnetic energy per unit volume is represented by

  • B22 μ0

  • B22 μ0 2

  • 2 B2μ0

  • B2μ0


243.

Magnetic field at ' 𝑎' distance a from long currying current wire is proportional to

  • 1𝑎

  • 1𝑎2

  • 1𝑎

  • 1𝑎32


244.

When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be

(i) a straight line  (ii) a circle  (iii) a helix

  • (i) only

  • (i) or (ii)

  • (i) or (iii)

  • any one of (i), (ii) and (iii)


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245.

Assertion: Magnetic field lines are continuous and closed.

Reason: Magnetic monopole does not exist.

  • If both assertion and reason are true but reason is not the correct explanation of assertion.

  • If both assertion and reason are true but reason is not the correct explanation of assertion.

  • If assertion is true but reason is false.

  • If both assertion and reason are false.


246.

Assertion:  Magnetic force between two short magnets, when they are co-axial follows inverse square law of distance. 

Reason:  The magnetic forces between two poles do not follow inverse square law of distance.

  • If both assertion and reason are true and reaon is correct explanation of assertion.

  • If both assertion and reason are true and reaon is not the correct explanation of assertion.

  • If assertion is true but reason is false.

  • If both assertion and reason are false.


247.

Assertion:  If  a proton and an a-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of a particle is double that of proton. 

Reason:  In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and is inversely proportional to charge of particle.

  • If both assertion and reason are true and reason is the correct explanation of assertion

  • If both assertion and reason are true but reason is not the correct explanation of assertion

  • If assertion is true but reason is false

  • If both assertion and reason are false.


248.

A  moving  coil  galvanometer  has  a resistance  of  900 Ω.  In order  to send  only 10 % of  the  main  current through  this  galvanometer,  the  resistance  of  the required  shunt  is

  • 0.9 Ω

  • 100 Ω

  • 405 Ω

  • 90 Ω


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249.

The intensity of magnetic field due to an isolated pole of strength mp at a point distant r from it will be

  • mp/r2

  • mp r2

  • r2/ mp

  • mp/r


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250.

The  ratio of magnetic fields on the axis of a circular current carrying coil of radius a to the magnetic field at its centre will be

  • 11 + x2a232

  • 11 + a2x212

  • 11 + a2x22

  • 11 + a2x23


A.

11 + x2a232

Consider a circular radius of a, carrying a current I. Consider a point P, which is at a distance x from the  centre of coil. We can consider that the loop is made p of a large number of short element, generating small magnetic fields. So the total field at P will be the sum of the contributions of all these elements. At the centre of coil, the field will be uniform.

By Biot- Savart’s law, the field dB due to a small element dl of the circle, centered at A is given by

       dB = μ04πdlx2 +a2

This can be resolved into two components, one along the axis OP, and other PS, which is perpendicular to OP. PS is exactly cancelled by the perpendicular component PS’ of the field due to a current and centered at A’. So, the total magnetic field at a point which is at a distance x away from the axis of a circular coil of radius a is given by,

       dB = μ0 I2 a2x2 + a232

 μ0, I are constants and by divide and multiply by a2 on denominator and numerator we get

       dB = 11 + x2a232


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