The magnetic field due to straight conductor of uniform cross-sec

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 Multiple Choice QuestionsMultiple Choice Questions

251.

Assertion:  When a radius of circular loop carrying current is doubled, its magnetic moment becomes four times.

Reason: Magnetic moment depends on area of the loop.

  • 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


252.

What is the magnetic field at a distance R from a coil of radius r carrying current ?

  • μ0 I R22  R2  +  r2 32

  • μ0I R22  R2 + r2 32

  • μ0 I2r

  • μ0 I2R


253.

In the following diagram, which particle has highest e/m value?

  

  • A

  • B

  • C

  • D


254.

Circular  loop  of  a  wire  and a  long  straight  wire  carry currents  Ic  and  Ie respectively  as shown in figure. Assuming  that  these  are  places  in  the same plane, the magnetic  field  will be  zero  at  the  centre of  the loop when separation  H is

  • Ie RIc π

  • Ic RIe π

  • π IcIe R

  • Ie πIc R


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255.

A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at I = 0 and completely emerges out at  t = T sec. The current in the ring varies as


256.

A conducting ring of radius 1 meter is placed in a uniform magnetic field B of 0.01 tesla oscillating with frequency 100 Hz with its plane at right angle to B. What will be the induced electric field?

  • π volts/m

  • 2 volts/m

  • 10 volts/m

  • 62 volts/m


257.

A proton and an  α -particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton α-particle is

  • 1 : 2

  • 1 : 4

  • 1 : 16

  • 4 : 1


258.

The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by


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259.

A circular coil of radius is R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a point on the axis of the coil located at a distance r from the centre of the coil, such that r >> R, varies as 

  • 1r

  • 1r32

  • 1r 2

  • 1r3


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260.

The magnetic field due to straight conductor of uniform cross-section of radius  ' a '  and carrying a steady current is represented by


A.

Here we can explain by three possible cases

Case (I):- Inside the straight conductor:

Take a surface inside the conductor of radius r.

then current enclosed this surface 

      i' = iπ a2 × πr2 

      i' = ir2a2

and length of wire

    dl = 2πr

from ampere circuital law,

   B.dl = μienclosed

     B × 2πr = μ × ir2a2

⇒       B = μ i r2πa2

Here it is clear that B is directly proportional to r.

So graph between B and r inside the conductor is straight line.

Case (II):- Surface of conductor

Enclosed current I = i

length of wire dl = 2πa

           B = μ i2πa

at surface of the conductor magnetic field intensity will be maximum 

e.g  μi2πa

Case (III):- outside the conductor

enclosed current = i

length of wire dl = 2πr

So, magnetic field

    B =  μi2πr

here it is clear that magnetic field is inverse proportional to r outside the conductor. So, graph between B and r the conductor will be hyperbolic.

Hence, option ( a) is correct choice.


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