A 2 A current carrying straight metal wire of resistance 1 , resistivity , area of cross-section 10 and mass 500 g is suspended horizontally in mid-air by applying a uniform magnetic field . The magnitude of B is

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Solution

Q.
A 2 A current carrying straight metal wire of resistance 1 $Ω$ , resistivity $2 \times 10^{- 6} Ω m$ , area of cross-section 10 $m m^{2}$ and mass 500 g is suspended horizontally in mid-air by applying a uniform magnetic field $\vec{B}$ . The magnitude of B is ____ $\times 10^{- 1} T$ (given, g = 10 m/s²) [2024]

Ans.
(5)    $R = \frac{ρ l}{A} \Rightarrow l = \frac{R A}{ρ} = \frac{1 \times 10 \times 10^{- 6}}{2 \times 10^{- 6}} = 5 m$

   $i l B = m g \Rightarrow B = \frac{m g}{i l}$

   $B = \frac{(0.5) (10)}{2 \times 5} = 5 \times 10^{- 1} T$

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