| A Helmholtz coil has pair of loops, each with \[N\] turns and radius\[R\]. They are placed coaxially at distance \[R\] and the same current \[I\] flows through the loops in the same direction. The magnitude of magnetic field at \[P\], midway between the centres \[A\]and \[C\], is given by (Refer to figure): [JEE Online 15-04-2018] |
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A) \[\frac{4N{{\mu }_{0}}I}{{{5}^{3/2}}R}\]
B) \[\frac{8N{{\mu }_{0}}I}{{{5}^{3/2}}R}\]
C) \[\frac{4N{{\mu }_{0}}I}{{{5}^{1/2}}R}\]
D) \[\frac{8N{{\mu }_{0}}I}{{{5}^{1/2}}R}\]
Correct Answer: B
Solution :
| [b] The magnetic field due to both the coils are in the same direction and equal in magnitude. |
| The magnitude of the magnetic field due to one coil is give as |
| \[B=\frac{{{\mu }_{o}}i{{R}^{2}}}{2{{({{R}^{2}}+{{(R/2)}^{2}})}^{3/2}}}\] |
| \[B=\frac{4{{\mu }_{o}}i{{R}^{2}}}{5{{R}^{2}}}\] |
| \[{{B}_{net}}=2B\] |
| \[{{B}_{net}}=\frac{8{{\mu }_{o}}i{{R}^{2}}}{5{{R}^{2}}}\] |
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