Two coaxial solenoids of different radii carry current I in the

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Two identical wires A and B, each of length ‘l’, carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side ‘a’. If BA and BB are the values of the magnetic field at the centres of the circle and square respectively, then the ratio BA /BB is:

  • straight pi squared over 8
  • fraction numerator straight pi squared over denominator 16 square root of 2 end fraction
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2.

Hysteresis loops for two magnetic materials A and B are given below:



These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:

  • A for electric generators and transformers.

  • A for electromagnets and B for electric generators

  • A for transformers and B for electric generators.

  • A for transformers and B for electric generators.

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3.

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

  • 80 H

  • 0.08 H

  • 0.044 H

  • 0.044 H

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4.

A galvanometer having a coil resistance of 100 Ω gives a full-scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full-scale deflection for a current of 10 A, is:

  • 0.01 Ω

  • 2 Ω

  • 0.1 Ω

  • 0.1 Ω

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5.

Two coaxial solenoids of different radii carry current I in the same direction. Let stack straight F subscript 1 with rightwards arrow on top be the magnetic force on the inner solenoid due to the outer one and stack straight F subscript 2 with rightwards arrow on top be the magnetic force on the outer solenoid due to the inner one. Then:

  • stack straight F subscript 1 space with rightwards arrow on top equals stack straight F subscript 2 space with rightwards arrow on top equals space 0
  • stack straight F subscript 1 with rightwards arrow on top is radially inwards and stack straight F subscript 2 with rightwards arrow on top is radially outwards
  • stack straight F subscript 1 with rightwards arrow on top is radially inwards and stack straight F subscript 2 with rightwards arrow on top =0
  • stack straight F subscript 1 with rightwards arrow on top is radially inwards and stack straight F subscript 2 with rightwards arrow on top =0


A.

stack straight F subscript 1 space with rightwards arrow on top equals stack straight F subscript 2 space with rightwards arrow on top equals space 0

Consider the two coaxial solenoids. Due to one of the solenoids magnetic field at the centre of the other can be assumed to be constant


Due to symmetry, forces on upper and lower part of the solenoid will be equal and opposite and hence resultant is zero.
Therefore option (a) is correct.

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6.

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below:



If there is a uniform magnetic field of 0.3 T in the positive z direction , in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

  • (a) and (b) respectively

  • (a) and (c) respectively

  • (b) and (d) respectively

  • (b) and (d) respectively

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7.

Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX' is given by

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8.

In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is

  • 250 Wb

  • 275 Wb

  • 200 Wb

  • 200 Wb

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9.

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB andCD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30º. Another straight thin wire with steady current I1 flowing out of the plane of the paper is kept at the origin.



The magnitude of the magnetic field (2) due to the loop ABCD at the origin (O) is

  • zero

  • fraction numerator straight mu space left parenthesis straight b minus straight a right parenthesis over denominator 24 ab end fraction
  • fraction numerator straight mu subscript straight o straight I over denominator 4 space straight pi end fraction space open square brackets fraction numerator straight b minus straight a over denominator ab end fraction close square brackets
  • fraction numerator straight mu subscript straight o straight I over denominator 4 space straight pi end fraction space open square brackets fraction numerator straight b minus straight a over denominator ab end fraction close square brackets
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10.

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB andCD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30º. Another straight thin wire with steady current I1 flowing out of the plane of the paper is kept at the origin.


Due to the presence of the current I1 at the origin


The magnitude of the magnetic field (2) due to the loop ABCD at the origin (O) is

  • The forces on AB and DC are zero

  • The forces on AD and BC are zero

  • The magnitude of the net force on the loop is given by fraction numerator straight mu subscript straight o II subscript 1 over denominator 4 straight pi end fraction space open square brackets 2 left parenthesis straight b minus straight a right parenthesis space plus space straight pi over 3 left parenthesis straight a plus straight b right parenthesis close square brackets

  • The magnitude of the net force on the loop is given by fraction numerator straight mu subscript straight o II subscript 1 over denominator 4 straight pi end fraction space open square brackets 2 left parenthesis straight b minus straight a right parenthesis space plus space straight pi over 3 left parenthesis straight a plus straight b right parenthesis close square brackets

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