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A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is :
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→B = μ0 I (μî × 2̂k) 4π r -
→B = - μ0 I (μî + 2̂k) 4π r -
→B = μ0 I (μî - 2̂k) 4π r -
→B = μ0 I (μî + 2̂k) 4π r
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Correct Option: B
Magnetic field due to segment ‘1’
| →B1 = | [sin 90° + sin 0°](-̂k) | |
| 4πR |
| = | (-̂k) = →B3 | |
| 4πR |
= Magnetic field due to segment 2
| B2 = | (-î) = | (πî) | ||
| 4R | 4πR |
∴ →B at centre
| →Bc = →B1 + →B2 + →B3 = | ((πî) + ̂k) | |
| 4πR |
