A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as <math> <mrow><mn>4</mn><mi>π</mi><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup>SI</mrow> </math> units):

The magnitude of magnetic field due to circular coil of N turns is given by B C = μ 0 i N 2 R <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> = 4 π × 1 0 − 7 × 7 × 1 0 0 2 × 0 . 1 <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> =4.4×10−3 T <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> =4.4mT <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]->

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as <math> <mrow><mn>4</mn><mi>π</mi><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup>SI</mrow> </math> &nbsp;units):

4.4 mT

44 mT

4.4 T

44 T

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Lenz's Law and Conservation of Energy Electromagnetic Induction Physics Class 12th

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 π \times 1 0^{- 7} SI$ units):

Option 1 -

44 mT

Option 2 -

4.4 T

Option 3 -

4.4 mT

Option 4 -

44 T

4 Views | Posted 2 months ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

The magnitude of magnetic field due to circular coil of $N$ turns is given by

$B_{C} = \frac{μ_{0} i N}{2 R}$

$= \frac{4 π \times 1 0^{- 7} \times 7 \times 100}{2 \times 0.1}$

$= 4.4 \times 1 0^{- 3} T$

$= 4.4 mT$

The magnitude of magnetic field due to circular coil of <math> <mrow> <mi>N</mi> </mrow> </math>  turns is given by <math> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mi>i</mi> <mi>N</mi> </mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816517993"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> <mo>×</mo> <mn>7</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>0</mn> <mo>.</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1816517994"> </o:OLEObject></xml><! [endif]-> <math> <mrow><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup> T</mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1816517995"> </o:OLEObject></xml><! [endif]-> <math> <mrow><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn>mT</mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1816517996"> </o:OLEObject></xml><! [endif]->

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A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 π \times 1 0^{- 7} SI$ units):

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A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4π×10−7SI units):

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A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A . The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 π \times 1 0^{- 7} SI$ units):