A long straight wire carrying a current of 30A is placed in an external uniform magnetic field of induction $4 \times 10^{- 4} T .$ The magnetic field is acting parallel to the direction of current The magnitude of the resultant magnetic induction $x \times 10^{- 4}$ in tesla at a point 2.0 cm away from the wire, what is value of ‘x’?

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answer is 5.

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Detailed Solution

Given magnetic field $B^{'} = 4 \times 10^{- 4} \hat{j}$

Magnetic field at ‘P’ due to straight wire
$B = \frac{μ_{0} i}{2 πr} = 3 \times 10^{- 4} T \otimes = 3 \times 10^{- 4} (- \hat{k})$
$∴ Resultent field at P is$
$\bar{B} = 4 \times 10^{- 4} \hat{j} - 3 \times 10^{- 4} \hat{k} = 5 \times 10^{- 4} T$

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