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Magnetic Field — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMagnetic Field3 Marks
Question
The shows a circular wire loop of radius a and carrying a current $i,$ which is placed in a perpendicular magnetic field $B.$
  1. Consider a small part $dl$ of the wire. Find the force on this part of the wire exerted by the magnetic field.
  2. Find the force of compression in the wire.
✓

Answer

  1. $\text{Fdl} = i \times dl \times B$ towards centre. $($By cross product rule$)$
  2. Let the length of subtends an small angle of $20$ at the centre.
Here, $2\text{T}\sin\theta=\text{i}\times\text{dl}\times\text{B}$
$\Rightarrow2\text{T}\theta=\text{i}\times\text{a}\times2\theta\times\text{B}$ $[\text{As}\theta\rightarrow0,\ \theta\approx0]$
$\Rightarrow\text{T}=\text{i}\times\text{a}\times\text{B}$
$\text{dl}=\text{a}\times2\theta$
Force of compression on the wire $=\text{i}\text{aB}$

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