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Question 27

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $$5.0$$ cm. The magnitude of the magnetic field at a point P midway between the wires is ______ $$\mu$$T. (Given: $$\mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}$$)

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Correct Answer: 160

$$B_{\text{net}} = B_1 + B_2 = 2 \times \left(\frac{\mu_0 I}{2\pi r}\right)$$

$$I = 10\text{ A},\quad d = 5.0\text{ cm} \implies r = \frac{d}{2} = 2.5\text{ cm} = 2.5 \times 10^{-2}\text{ m}$$

$$B_{\text{net}} = 2 \times \frac{4\pi \times 10^{-7} \times 10}{2\pi \times 2.5 \times 10^{-2}} \implies B_{\text{net}} = 1.6 \times 10^{-4}\text{ T} = 160\ \mu\text{T}$$

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