Moving Charges And Magnetism

Sponsor Area

Question
CBSEENPH12040010

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane.  if the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre is

  • fraction numerator straight mu subscript straight o space straight i over denominator 2 square root of 2 straight R end root end fraction
  • fraction numerator straight mu subscript 0 straight i over denominator 2 straight R end fraction
  • fraction numerator straight mu subscript straight o straight i over denominator 4 straight R end fraction
  • fraction numerator straight mu subscript straight o straight i over denominator square root of 2 straight R end fraction

Solution

A.

fraction numerator straight mu subscript straight o space straight i over denominator 2 square root of 2 straight R end root end fraction straight B subscript 1 space equals space straight B subscript 2 space equals space fraction numerator straight mu subscript 0 straight i over denominator 4 straight R end fraction
The space magnetic space field space at space their space common space centre
bold B with bold rightwards arrow on top bold space bold equals bold space stack bold B subscript bold 1 with bold rightwards arrow on top bold space bold plus bold space stack bold B subscript bold 2 with bold rightwards arrow on top
straight B space equals space square root of straight B subscript 1 superscript 2 plus straight B subscript 2 superscript 2 end root
space equals square root of open parentheses fraction numerator straight mu subscript straight o straight i over denominator 4 straight R end fraction close parentheses squared plus open parentheses fraction numerator straight mu subscript 0 straight i over denominator 4 straight R end fraction close parentheses squared end root
equals space straight B space fraction numerator straight mu subscript 0 straight i over denominator 2 square root of 2 straight R end root end fraction

Sponsor Area

Question
CBSEENPH12039984

A galvanometer has a coil of resistance 100 Ω and gives a full-scale deflection for 30 mA current. If it is to work as a voltmeter of 30 V range, the resistance required to be added will be

  • 900 Ω

  • 1800

  • 500 Ω

  • 1000 Ω

Solution

A.

900 Ω

Required resistance
straight R space equals space straight V over straight i subscript straight g minus space straight G

equals space fraction numerator 30 over denominator 30 space straight x space 10 to the power of negative 3 end exponent end fraction space minus space 100 space equals space 900 space straight capital omega

Question
CBSEENPH12040065

A galvanometer of resistance 50 Ω is connected to a battery of 3 V along with a resistance of 2950 Ω in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be

  • 5050 Ω

  • 5550 Ω

  • 6050 Ω

  • 4450 Ω

Solution

D.

4450 Ω

Current through the galvanometer 

space straight I thin space equals space fraction numerator 3 over denominator left parenthesis 50 plus 2950 right parenthesis end fraction space equals space 10 to the power of negative 3 end exponent space straight A
Current space for space 30 space divisions space equals space 10 to the power of negative 3 end exponent space straight A
Current space for space 20 space divisions space equals space 10 to the power of negative 3 end exponent over 30 space straight x space 20
equals space 2 over 3 space straight x space 10 to the power of negative 3 end exponent space straight A
For space the space same space deflection space to space obtain space for space 20 space divisions comma let space resistance space added space be space straight R
therefore comma
2 over 3 space straight x space 10 to the power of negative 3 end exponent space equals space fraction numerator 3 over denominator left parenthesis 50 plus 1 straight R right parenthesis end fraction
Or space straight R space equals space 4450 space straight capital omega

Question
CBSEENPH12039961

A galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged,the resistance to be put in series with the galvanometer is

  • fraction numerator straight S squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction
  • fraction numerator SG over denominator left parenthesis straight S plus straight G right parenthesis end fraction
  • fraction numerator straight G squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction
  • fraction numerator straight G over denominator left parenthesis straight S plus straight G right parenthesis end fraction

Solution

C.

fraction numerator straight G squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction

Current will be unchanged if resistance remains same so


straight G space equals space fraction numerator GS over denominator straight G space plus straight S end fraction space plus straight R
straight R space equals space straight G space minus space fraction numerator GS over denominator straight G space plus straight S end fraction
straight R space equals space fraction numerator straight G squared over denominator straight G space plus straight S end fraction

Question
CBSEENPH12040058

A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 x 10-3 Wb. The self -inductance of the solenoid is 

  • 2.5 H

  • 2.0 H

  • 1.0 H

  • 4.0 H

Solution

C.

1.0 H

The inductance of a coil is numerically equal to the emf induced in the coil when the current in the coil changes at the rate of 1 As-1. If I is the current flowing in the circuit, then flux linked with the circuit is observed to be proportional to I, ie,
straight ϕ space proportional to space straight I
straight ϕ space equals space LI space... space left parenthesis straight i right parenthesis
where L is called the self-inductance or coefficients of self-inductance or coefficient of self-inductance or simply inductance of the coil.
Net flux through the solenoid.
Φ = 500 x 4 x 10-3 = 2 Wb
Or 2 = L x 2 [after putting value in eq. or  L = 1H]

23