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| Numerical 04 |
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| 04. A solenoid 50cm long has 4 layers of windings of 350 turns each. The radius of the lowest layer is 1.4cm. If the current carries is 6.0A, estimate the magnitude of B |
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| (a) near the centre of the solenoid on it's axis and off it's axis |
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| (b) near it's ends on it's axis |
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| (c) outside the solenoid near it's centre. |
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| Suggested solution: |
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| The ratio of length to radius of the solenoid is quite large (nearly 35). So, to estimate B approximately, we can employ the exact results for a closely wound infinitely long solenoid. |
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| where n is the number of turns per meter length of the solenoid. It may be noted that the radius of the wire does not enter this equation. So, n can be obtained by simply multiplying the number of turns per layer by the number of layers and dividing the product by the length of the solenoid. |
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| It may be noted here that this estimate of B is for both on and off the axis. This is because for an infinitely long solenoid, the internal field near the centre is uniform over the entire cross-section. |
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| (b) At the ends of the solenoid, |
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| (c) The outside field near the centre of a long solenoid is negligible compared to the internal field. |
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