4.11 In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s^–1normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.

(e = 1.6 × 10^–19 C, me = 9.1×10^–31 kg)

4 Views | Posted 5 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

5 months ago

4.11 Magnetic field strength, B = 6.5 G = 6.5 $\times 10^{- 4}$ T

Speed of electron, v = 4.8 $\times 10^{6}$ m/s

Charge of electron, e = 1.6 $\times 10^{- 19}$ C

Mass of electron, m = 9.1 $\times 10^{- 31}$ kg

Angle between the shot electron and the magnetic field, $θ$ = 90 $°$

Magnetic force exerted on the electron in the magnetic field is given as:

F = evB $\sin ? θ$

This force provides centripetal force to the moving electron. Hence, the electron starts moving in a circular path of radius r

The centripetal force exerted on electron, $F_{c}$ = $\frac{m v^{2}}{r}$

In equilibrium, the centripetal force exerted on electron = magnetic force on the electron

F = $F_{c}$

evB $\sin ? θ = \frac{m v^{2}}{r}$

r = $\frac{m v}{e B \sin ? θ}$ = $\frac{9.1 \times 10^{- 31} \times 4.8 \times 10^{6}}{1.6 \times 10^{- 19} \times 6.5 \times 10^{- 4} \times s i n 90 °}$ = 4.20 $\times 10^{- 2}$ m = 4.20 cm

4.11 Magnetic field strength, B = 6.5 G = 6.5 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </math> TSpeed of electron, v = 4.8 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> </math> m/sCharge of electron, e = 1.6 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </mrow> </msup> </math> CMass of electron, m = 9.1 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>31</mn> </mrow> </mrow> </msup> </math> kgAngle between the shot electron and the magnetic field, <math> <mi>θ</mi> </math> = 90 <math> <mo>°</mo> </math> Magnetic force exerted on the electron in the magnetic field is given as:F = evB <math> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>?</mo> <mrow> <mi>θ</mi> </mrow> </mrow> </math> This force provides centripetal force to the moving electron. Hence, the electron starts moving in a circular path of radius rThe centripetal force exerted on electron, <math> <msub> <mrow> <mrow> <mi>F</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </msub> </math> = <math> <mfrac> <mrow> <mrow> <mi>m</mi> <msup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> </math> In equilibrium, the centripetal force exerted on electron = magnetic force on the electronF = <math> <msub> <mrow> <mrow> <mi>F</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </msub> </math> evB <math> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>?</mo> <mrow> <mi>θ</mi> </mrow> </mrow> <mo>=</mo> <mi> </mi> <mfrac> <mrow> <mrow> <mi>m</mi> <msup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> </math> r = <math> <mfrac> <mrow> <mrow> <mi>m</mi> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">B</mi> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>?</mo> <mrow> <mi>θ</mi> </mrow> </mrow> </mrow> </mrow> </mfrac> </math> = <math> <mfrac> <mrow> <mrow> <mn>9.1</mn> <mi mathvariant="normal"> </mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>31</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>4.8</mn> <mi mathvariant="normal"> </mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>1.6</mn> <mi mathvariant="normal"> </mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>6.5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> <mo>×</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>90</mn> <mo>°</mo> </mrow> </mrow> </mfrac> </math> = 4.20 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> m = 4.20 cm

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question