Physics-
General
Easy

Question

A small coil C with N = 200 turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in figure. The cross sectional area of coil is A= 1.0 cm2, length of arm OA of the balance beam is l equals 30 c m. When there is no current in the coil the balance is in equilibrium. On passing a current I = 22 mA through the coil the equilibrium is restored by putting the additional counter weight of mass capital delta m equals 60 m g on the balance pan. Find the magnetic induction at the spot where coil is located.

  1. 0.4 T    
  2. 0.3 T    
  3. 0.2 T    
  4. 0.1 T    

The correct answer is: 0.4 T


    On passing current through the coil, it acts as a magnetic dipole. Torque acting on magnetic dipole is counter balanced by the moment of additional weight about position O. Torque acting on a magnetic dipole
    tau equals M B sin invisible function application theta equals left parenthesis N i A right parenthesis B sin invisible function application 9 0 to the power of o end exponent equals N i A B.
    Again tau equals F o r c e cross times L e v e r   a r m   equals capital delta m g cross times l
    rightwards double arrow N i A B equals capital delta m g l
    rightwards double arrow B equals fraction numerator capital delta m g l over denominator N i A end fraction equals fraction numerator 60 cross times 1 0 to the power of negative 3 end exponent cross times 9.8 cross times 30 cross times 1 0 to the power of negative 2 end exponent over denominator 200 cross times 22 cross times 1 0 to the power of negative 3 end exponent cross times 1 cross times 1 0 to the power of negative 4 end exponent end fraction= 0.4 T

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