Q: A charge of 8.85 \times 10^{-12}\text{ C} is enclosed by a closed surface. The total flux through it is:

1\text{ N}\cdot\text{m}^2/\text{C}. \Phi = \dfrac{q}{\varepsilon_0} = \dfrac{8.85 \times 10^{-12}}{8.85 \times 10^{-12}} = 1\text{ N}\cdot\text{m}^2/\text{C}.

Q: A uniform field E = 2000\text{ N/C} passes through a rectangular surface 10\text{ cm} \times 20\text{ cm} whose normal makes 60^\circ with the field. The flux is:

20\text{ N}\cdot\text{m}^2/\text{C}. \Phi = EA\cos\theta = 2000 \times 0.02 \times \cos 60^\circ = 40 \times 0.5 = 20\text{ N}\cdot\text{m}^2/\text{C}.

Question 1

Gauss' law states that the total electric flux through a closed surface equals:

Accepted Answer

The charge enclosed divided by \varepsilon_0. \oint \vec{E}\cdot d\vec{A} = \dfrac{q_{enc}}{\varepsilon_0}, where only charges inside the surface contribute.

Question 2

The electric flux through a closed surface enclosing a given charge depends on:

Accepted Answer

Only the magnitude of the enclosed charge. Gauss' law makes the flux independent of the geometry, which is what makes it such a powerful shortcut.

Question 3

The electric field due to an infinite plane sheet of surface charge density \sigma is:

Accepted Answer

\dfrac{\sigma}{2\varepsilon_0}, independent of distance. A Gaussian cylinder gives a uniform field on both sides, which does not weaken with distance from the sheet.

Question 4

The electric field at any point inside a uniformly charged conducting spherical shell is:

Accepted Answer

Zero. A Gaussian surface drawn inside encloses no charge, so the field must vanish everywhere within.

Question 5

The electric field outside a uniformly charged spherical shell of total charge Q at distance r from the centre is:

Accepted Answer

\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^2}. Outside the shell the field is exactly as though all the charge were concentrated at the centre.

Question 6

The electric field due to an infinitely long straight charged wire of linear charge density \lambda at distance r is proportional to:

Accepted Answer

\dfrac{1}{r}. A cylindrical Gaussian surface gives E = \dfrac{\lambda}{2\pi\varepsilon_0 r}.

Question 7

The net electric flux through a closed surface that encloses no net charge is:

Accepted Answer

Zero. Whatever flux enters the surface must leave it, so the net flux is zero even if the field inside is not.

Question 8

Electric flux is a:

Accepted Answer

Scalar quantity. It is defined by the scalar product \vec{E}\cdot d\vec{A}, and its unit is 	ext{N}\cdot	ext{m}^2/	ext{C}.

Question 9

A charge of 8.85 	imes 10^{-12}	ext{ C} is enclosed by a closed surface. The total flux through it is:

Accepted Answer

1	ext{ N}\cdot	ext{m}^2/	ext{C}. \Phi = \dfrac{q}{\varepsilon_0} = \dfrac{8.85 	imes 10^{-12}}{8.85 	imes 10^{-12}} = 1	ext{ N}\cdot	ext{m}^2/	ext{C}.

Question 10

A uniform field E = 2000	ext{ N/C} passes through a rectangular surface 10	ext{ cm} 	imes 20	ext{ cm} whose normal makes 60^\circ with the field. The flux is:

Accepted Answer

20	ext{ N}\cdot	ext{m}^2/	ext{C}. \Phi = EA\cos	heta = 2000 	imes 0.02 	imes \cos 60^\circ = 40 	imes 0.5 = 20	ext{ N}\cdot	ext{m}^2/	ext{C}.

Question 11

A point charge q is placed at the centre of a cube. The flux through one face of the cube is:

Accepted Answer

\dfrac{q}{6\varepsilon_0}. The total flux \dfrac{q}{\varepsilon_0} is shared equally among the six identical faces.

Question 12

An infinite sheet carries a surface charge density of 8.85 	imes 10^{-12}	ext{ C/m}^2. The field near it is:

Accepted Answer

0.5	ext{ N/C}. E = \dfrac{\sigma}{2\varepsilon_0} = \dfrac{8.85 	imes 10^{-12}}{2 	imes 8.85 	imes 10^{-12}} = 0.5	ext{ N/C}.

Question 13

An infinitely long wire has a linear charge density of 10^{-6}	ext{ C/m}. The field at 0.1	ext{ m} from it is:

Accepted Answer

1.8 	imes 10^5	ext{ N/C}. E = \dfrac{2k\lambda}{r} = \dfrac{2 	imes 9 	imes 10^9 	imes 10^{-6}}{0.1} = 1.8 	imes 10^5	ext{ N/C}.

Question 14

A spherical shell of radius 0.1	ext{ m} carries a charge of 1\,\mu	ext{C}. The field at a point 0.2	ext{ m} from its centre is:

Accepted Answer

2.25 	imes 10^5	ext{ N/C}. Outside the shell it behaves as a point charge: E = \dfrac{9 	imes 10^9 	imes 10^{-6}}{(0.2)^2} = 2.25 	imes 10^5	ext{ N/C}.

Question 15

A spherical shell carries a charge Q. The electric field at a point inside the shell is:

Accepted Answer

Zero. A Gaussian sphere drawn inside encloses no charge, so by symmetry the field is zero everywhere within.

Question 16

A closed surface encloses charges of +2\,\mu	ext{C} and -2\,\mu	ext{C}. The total flux through it is:

Accepted Answer

Zero. The net enclosed charge is zero, so by Gauss' law the total flux is zero.

Question 17

A uniform field of 100	ext{ N/C} passes normally through an area of 2	ext{ m}^2. The flux is:

Accepted Answer

200	ext{ N}\cdot	ext{m}^2/	ext{C}. \Phi = EA\cos 0^\circ = 100 	imes 2 = 200	ext{ N}\cdot	ext{m}^2/	ext{C}.

Question 18

The flux through a closed surface is 100	ext{ N}\cdot	ext{m}^2/	ext{C}. The charge enclosed is:

Accepted Answer

8.85 	imes 10^{-10}	ext{ C}. q = \varepsilon_0\Phi = 8.85 	imes 10^{-12} 	imes 100 = 8.85 	imes 10^{-10}	ext{ C}.

Question 19

A charge is enclosed by a spherical Gaussian surface. If the radius of the sphere is doubled, the flux through it:

Accepted Answer

Remains unchanged. Gauss' law makes the flux depend only on the enclosed charge, not on the size of the surface.

Question 20

A spherical shell of radius 0.2	ext{ m} carries a charge of 4\,\mu	ext{C}. The field just outside its surface is:

Accepted Answer

9 	imes 10^5	ext{ N/C}. E = \dfrac{9 	imes 10^9 	imes 4 	imes 10^{-6}}{(0.2)^2} = \dfrac{3.6 	imes 10^4}{0.04} = 9 	imes 10^5	ext{ N/C}.

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