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Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me?
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Radius of a current carrying coil is R. the ratio of magnetic field at...
Explanation:
1. Formula for magnetic field at the axial point:
According to the Biot-Savart law, the magnetic field at an axial point of a current-carrying coil is given by:
\[ B_{axial} = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} \]
2. Formula for magnetic field at the center of the coil:
The magnetic field at the center of the coil is given by:
\[ B_{center} = \frac{\mu_0 I}{2R} \]
3. Ratio of magnetic fields:
To find the ratio of magnetic fields at the axial point and the center of the coil, we divide the two equations:
\[ \frac{B_{axial}}{B_{center}} = \frac{\frac{\mu_0 I R^2}{2(R^2 + R^2)^{3/2}}}{\frac{\mu_0 I}{2R}} \]
\[ = \frac{R}{(2R^2)^{3/2}} = \frac{R}{2\sqrt{R^3}} = \frac{1}{2\sqrt{R}} = \frac{1}{2} \cdot R^{-1/2} \]
4. Answer:
Therefore, the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil is \( \frac{1}{2} \cdot R^{-1/2} \) or \( \frac{1}{2^{3/2}} \), which is option (3) \( \left(\frac{1}{2}\right)^{3/2} \).
1. Formula for magnetic field at the axial point:
According to the Biot-Savart law, the magnetic field at an axial point of a current-carrying coil is given by:
\[ B_{axial} = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} \]
2. Formula for magnetic field at the center of the coil:
The magnetic field at the center of the coil is given by:
\[ B_{center} = \frac{\mu_0 I}{2R} \]
3. Ratio of magnetic fields:
To find the ratio of magnetic fields at the axial point and the center of the coil, we divide the two equations:
\[ \frac{B_{axial}}{B_{center}} = \frac{\frac{\mu_0 I R^2}{2(R^2 + R^2)^{3/2}}}{\frac{\mu_0 I}{2R}} \]
\[ = \frac{R}{(2R^2)^{3/2}} = \frac{R}{2\sqrt{R^3}} = \frac{1}{2\sqrt{R}} = \frac{1}{2} \cdot R^{-1/2} \]
4. Answer:
Therefore, the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil is \( \frac{1}{2} \cdot R^{-1/2} \) or \( \frac{1}{2^{3/2}} \), which is option (3) \( \left(\frac{1}{2}\right)^{3/2} \).
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Radius of a current carrying coil is R. the ratio of magnetic field at...
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Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me?
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Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me?.
Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of a current carrying coil is R. the ratio of magnetic field at an axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil ? Options:- (1)(1/2) to the power 1/2. (2)1/2. (3)(1/2) to the power 3/2 (4)1/4 Correct option is 3. How ? Please help me?.
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