# Derive dimensions of magnetic induction

1
by namku

2015-04-14T21:11:38+05:30

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We have the formula  for a force acting on a current carrying conductor.

B = magnetic induction = magnetic field strength.
Force =  B I L      ie.,  current = I    length  = L  force = newtons.
let dimensions of current be [ A ]
M L T⁻² =  B  A  L

B = [ M T⁻² A⁻¹ ]
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we have the formula for magnetic field strength at a point d distance away from a current carrying conductor  as :

B = μ₀ I / (2 π d)        this is found by Ampere's circuital law.
μ₀ =  Newtons/Ampere²

B = M L T⁻²  A⁻²   * A  L⁻¹

dimensions      = M T⁻² A⁻¹
units         =  Tesla  or  kg / sec²-Amp        or  Newtons/Amp-meter