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  • 20-01-2020
  • Physics
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2. Show that the total force on a closed circuit carrying a current I in a uniform magnetic field is zero. The circuit is made of thin wires.

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Manetho
Manetho Manetho
  • 21-01-2020

Explanation:

FOR CLOSED CIRCUIT LOOP IN  A UNIFORM MAGNETIC FIELD

total force F= [tex]I\oint\vec{ds}\times\vec{B}[/tex]

here vector B has constant strength and direction so, we take it outside the integral

F= [tex]I\times\vec{B}\oint\vec{ds}[/tex]

[tex]\oint\vec{ds}[/tex]= This vector displacements yields overall displacement

so, [tex]\oint\vec{ds}[/tex]=0

therefore,

F= [tex]I\times\vec{B}\oint\vec{ds}[/tex]=0

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