1.20 A point charge causes an electric flux of –1.0 $\times 10^{3}$ N $m^{2}$ /C to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge.

(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

(b) What is the value of the point charge?

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alok kumar singh | Contributor-Level 10

3 months ago

1.20 Electric flux, $φ$ = –1.0 $\times 10^{3}$ N $m^{2}$ /C

Radius of Gaussian surface, r = 10 cm = 0.1 m

(a) Electric flux piercing through a surface depends on the net charge enclosed inside a body, not on the size of the body. Hence, if the radius is doubled, the net flux passing does not change. The net flux passing will remain as -1 N $\times 10^{3}$ N $m^{2}$ /C

(b) The relation between point charge and the electric flux is given by $φ$ = $\frac{q}{?_{0}},$

Where $?_{0}$ = Permittivity of free space = 8.854 × $10^{- 12}$ $C^{2} N^{- 1}$ $m^{- 2}$

Hence point charge q = φ $\times$ $?_{0}$ = –1.0 $\times 10^{3} \times$ 8.854 $\times 10^{- 12}$ C = - 8.854 $\times 10^{- 9}$ C

= - 8.854 $\times 10^{- 3} μ$ C

1.20 Electric flux, <math><mi>φ</mi></math>= –1.0 <math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math> N<math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math>/CRadius of Gaussian surface, r = 10 cm = 0.1 m(a) Electric flux piercing through a surface depends on the net charge enclosed inside a body, not on the size of the body. Hence, if the radius is doubled, the net flux passing does not change. The net flux passing will remain as -1  N<math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math> N<math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></math>/C (b) The relation between point charge and the electric flux is given by <math><mi>φ</mi></math>=<math><mfrac><mrow><mrow><mi>q</mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac><mo>,</mo></math>Where <math><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math>= Permittivity of free space = 8.854 ×<math><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>12</mn></mrow></mrow></msup></math> <math><msup><mrow><mrow><mi>C</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><msup><mrow><mrow><mi>N</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow></msup></math><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></math>Hence point charge q = φ<math><mi></mi><mo>×</mo></math> <math><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math>= –1.0 <math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup><mo>×</mo></math> 8.854 <math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>12</mn></mrow></mrow></msup></math> C = - 8.854 <math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>9</mn></mrow></mrow></msup></math> C= - 8.854<math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>3</mn><mi></mi></mrow></mrow></msup><mi>μ</mi></math>C

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1.20 A point charge causes an electric flux of –1.0 ×103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?