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Q.

A long straight wire carrying current of 30 A is placed in an external uniform magnetic field of induction 4 × 10^–4T. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point 2.0 cm away from the wire is

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a

10^–4

b

3 × 10^–4

c

5 × 10^–4

d

6 × 10^–4

answer is C.

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Detailed Solution

$\begin{array}{l} B_{1} = \frac{μ_{0} i}{2 πr} = \frac{4 π \times 10^{- 7} \times 30}{2 π \times 2 \times 10^{- 2}} = 3 \times 10^{- 4} T \\ B_{2} = 4 \times 10^{- 4} T (given) \end{array}$
Resultant magnetic induction
$B = \sqrt{B_{1}^{2} + B_{2}^{2}} = 5 \times 10^{- 4} T$

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