Magnetic force

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Question

A straight wire of length 30cm and mass 6mg lies in a direction $30^{0}$ east of north. The earth’s field at this site is horizontal and has a magnitude of 0.8G. The current must be passed through the wire so that it may float in air is ( $g = 10 {ms}^{- 2}$ ) ……..A.

Moderate

Solution

$G r a v i t a t i o n a l f o r c e s h o u l d b e b a l a n c e d b y m a g n e t i c f o r c e o n w i r e, \Rightarrow m g = B i l s i n θ \Rightarrow i = \frac{m g}{B l s i n θ} = \frac{6 \times 10^{- 6} \times 10}{0.8 \times 10^{- 4} \times 0.3 \times \frac{1}{2}} = 5 A$

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