4.25 A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the

(a) total torque on the coil,

(b) total force on the coil,

(c) average force on each electron in the coil due to the magnetic field?

(The coil is made of copper wire of cross-sectional area 10^–5 m², and the free electron density in copper is given to be about 1029 m^–3.)

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Payal Gupta | Contributor-Level 10

5 months ago

4.25 Number of turns on the circular coil, n =20

Radius of the coil, r = 10 cm = 0.1 m

Magnetic field strength, B = 0.10 T

Current in the coil, I = 5.0 A

The total torque on the coil is zero because the field is uniform.

Cross-sectional area of the copper coil, A = $10^{- 5}$ $m^{2}$

Number of free electrons per cubic meter of copper, N = $10^{29}$ / $m^{3}$

Charge on the electron, e = 1.6 $\times 10^{19}$ C

Magnetic force, F = Be $v_{d}$ where $v_{d}$ is the drift velocity of electrons

$v_{d} = \frac{I}{N e A}$ $μ_{0}$

$H e n c e F$ = $\frac{B e I}{N e A}$ = $\frac{0.1 \times 5}{10^{29} \times 10^{- 5}}$ = 5 $\times 10^{- 25}$ N

The average force on each electron is 5 $\times 10^{- 25}$ N

4.25 Number of turns on the circular coil, n =20Radius of the coil, r = 10 cm = 0.1 mMagnetic field strength, B = 0.10 TCurrent in the coil, I = 5.0 AThe total torque on the coil is zero because the field is uniform.The total torque on the coil is zero because the field is uniform.Cross-sectional area of the copper coil, A = <math> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> </math> <math> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> Number of free electrons per cubic meter of copper, N = <math> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>29</mn> </mrow> </mrow> </msup> </math> / <math> <msup> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </math> Charge on the electron, e = 1.6 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>19</mn> </mrow> </mrow> </msup> </math> CMagnetic force, F = Be <math> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> </msub> </math> where <math> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> </msub> </math> is the drift velocity of electrons <math> <msub> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi> </mi> <mfrac> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>N</mi> <mi>e</mi> <mi>A</mi> </mrow> </mrow> </mfrac> </math> <math> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> <math> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi> </mi> <mi>F</mi> </math> = <math> <mfrac> <mrow> <mrow> <mi>B</mi> <mi>e</mi> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mi>N</mi> <mi>e</mi> <mi>A</mi> </mrow> </mrow> </mfrac> </math> = <math> <mfrac> <mrow> <mrow> <mn>0.1</mn> <mo>×</mo> <mn>5</mn> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>29</mn> </mrow> </mrow> </msup> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> = 5 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>25</mn> </mrow> </mrow> </msup> </math> NThe average force on each electron is 5 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>25</mn> </mrow> </mrow> </msup> </math> N

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