Electric flux through a closed surface and Gauss’s Law
PHXII01:ELECTRIC CHARGES AND FIELDS

358308 A cubical Gaussian surface has side of length \(a = 10\;cm\). Electric field lines are parallel to \(x - \)axis as shown. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are \(6 k N C^{-1}\) and \(9 k N C^{-1}\) respectively. Then the total charge enclosed by the cube is \(\left[ {{\rm{Take}}\,\,{\varepsilon _0} = 9 \times {{10}^{ - 12}}F{m^{ - 1}}} \right]\)
supporting img

1 \( - 1.35{\rm{ }}n{\rm{ }}C\)
2 \(0.27{\rm{ }}n{\rm{ }}C\)
3 \( - 0.27{\rm{ }}n{\rm{ }}C\)
4 \(1.35{\rm{ }}n{\rm{ }}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358309 The inward and outward electric flux for a closed surface in units of \(N - {m^2}{\text{/}}C\) are respectively \(8 \times {10^3}\) and \(4 \times {10^3}\) . Then the total charge inside the surface is [where \({\varepsilon _0} = \) permittivity constant]

1 \(4 \times {10^3}C\)
2 \( - 4 \times {10^3}C\)
3 \(\frac{{\left( { - 4 \times {{10}^3}} \right)C}}{{{\varepsilon _0}}}\)
4 \( - 4 \times {10^3}{\varepsilon _0}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358310 If there is only one type of charge in the universe, then (\(\overrightarrow E = \) Electric field, \(d\overrightarrow S = \) Area vector)

1 \(\oint {\overrightarrow E } .d\overrightarrow S \ne 0\) on any surface
2 \(\oint {\overrightarrow E } .d\overrightarrow S \) could not be defined
3 \(\oint {\overrightarrow E } .d\overrightarrow S \ne \propto \) if charge is inside
4 \(\oint {\overrightarrow E } .d\overrightarrow S = 0\) if charge is outside, \(\frac{q}{{{\varepsilon _0}}}\) if charge is inside
PHXII01:ELECTRIC CHARGES AND FIELDS

358311 Electric flux emanating through a surface element \(d\vec S = 5\,\hat i\) placed in an electric field \(\vec E = 4\hat i + 4\hat j + 4\hat k\) is

1 10 units
2 20 units
3 4 units
4 16 units
PHXII01:ELECTRIC CHARGES AND FIELDS

358308 A cubical Gaussian surface has side of length \(a = 10\;cm\). Electric field lines are parallel to \(x - \)axis as shown. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are \(6 k N C^{-1}\) and \(9 k N C^{-1}\) respectively. Then the total charge enclosed by the cube is \(\left[ {{\rm{Take}}\,\,{\varepsilon _0} = 9 \times {{10}^{ - 12}}F{m^{ - 1}}} \right]\)
supporting img

1 \( - 1.35{\rm{ }}n{\rm{ }}C\)
2 \(0.27{\rm{ }}n{\rm{ }}C\)
3 \( - 0.27{\rm{ }}n{\rm{ }}C\)
4 \(1.35{\rm{ }}n{\rm{ }}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358309 The inward and outward electric flux for a closed surface in units of \(N - {m^2}{\text{/}}C\) are respectively \(8 \times {10^3}\) and \(4 \times {10^3}\) . Then the total charge inside the surface is [where \({\varepsilon _0} = \) permittivity constant]

1 \(4 \times {10^3}C\)
2 \( - 4 \times {10^3}C\)
3 \(\frac{{\left( { - 4 \times {{10}^3}} \right)C}}{{{\varepsilon _0}}}\)
4 \( - 4 \times {10^3}{\varepsilon _0}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358310 If there is only one type of charge in the universe, then (\(\overrightarrow E = \) Electric field, \(d\overrightarrow S = \) Area vector)

1 \(\oint {\overrightarrow E } .d\overrightarrow S \ne 0\) on any surface
2 \(\oint {\overrightarrow E } .d\overrightarrow S \) could not be defined
3 \(\oint {\overrightarrow E } .d\overrightarrow S \ne \propto \) if charge is inside
4 \(\oint {\overrightarrow E } .d\overrightarrow S = 0\) if charge is outside, \(\frac{q}{{{\varepsilon _0}}}\) if charge is inside
PHXII01:ELECTRIC CHARGES AND FIELDS

358311 Electric flux emanating through a surface element \(d\vec S = 5\,\hat i\) placed in an electric field \(\vec E = 4\hat i + 4\hat j + 4\hat k\) is

1 10 units
2 20 units
3 4 units
4 16 units
PHXII01:ELECTRIC CHARGES AND FIELDS

358308 A cubical Gaussian surface has side of length \(a = 10\;cm\). Electric field lines are parallel to \(x - \)axis as shown. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are \(6 k N C^{-1}\) and \(9 k N C^{-1}\) respectively. Then the total charge enclosed by the cube is \(\left[ {{\rm{Take}}\,\,{\varepsilon _0} = 9 \times {{10}^{ - 12}}F{m^{ - 1}}} \right]\)
supporting img

1 \( - 1.35{\rm{ }}n{\rm{ }}C\)
2 \(0.27{\rm{ }}n{\rm{ }}C\)
3 \( - 0.27{\rm{ }}n{\rm{ }}C\)
4 \(1.35{\rm{ }}n{\rm{ }}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358309 The inward and outward electric flux for a closed surface in units of \(N - {m^2}{\text{/}}C\) are respectively \(8 \times {10^3}\) and \(4 \times {10^3}\) . Then the total charge inside the surface is [where \({\varepsilon _0} = \) permittivity constant]

1 \(4 \times {10^3}C\)
2 \( - 4 \times {10^3}C\)
3 \(\frac{{\left( { - 4 \times {{10}^3}} \right)C}}{{{\varepsilon _0}}}\)
4 \( - 4 \times {10^3}{\varepsilon _0}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358310 If there is only one type of charge in the universe, then (\(\overrightarrow E = \) Electric field, \(d\overrightarrow S = \) Area vector)

1 \(\oint {\overrightarrow E } .d\overrightarrow S \ne 0\) on any surface
2 \(\oint {\overrightarrow E } .d\overrightarrow S \) could not be defined
3 \(\oint {\overrightarrow E } .d\overrightarrow S \ne \propto \) if charge is inside
4 \(\oint {\overrightarrow E } .d\overrightarrow S = 0\) if charge is outside, \(\frac{q}{{{\varepsilon _0}}}\) if charge is inside
PHXII01:ELECTRIC CHARGES AND FIELDS

358311 Electric flux emanating through a surface element \(d\vec S = 5\,\hat i\) placed in an electric field \(\vec E = 4\hat i + 4\hat j + 4\hat k\) is

1 10 units
2 20 units
3 4 units
4 16 units
PHXII01:ELECTRIC CHARGES AND FIELDS

358308 A cubical Gaussian surface has side of length \(a = 10\;cm\). Electric field lines are parallel to \(x - \)axis as shown. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are \(6 k N C^{-1}\) and \(9 k N C^{-1}\) respectively. Then the total charge enclosed by the cube is \(\left[ {{\rm{Take}}\,\,{\varepsilon _0} = 9 \times {{10}^{ - 12}}F{m^{ - 1}}} \right]\)
supporting img

1 \( - 1.35{\rm{ }}n{\rm{ }}C\)
2 \(0.27{\rm{ }}n{\rm{ }}C\)
3 \( - 0.27{\rm{ }}n{\rm{ }}C\)
4 \(1.35{\rm{ }}n{\rm{ }}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358309 The inward and outward electric flux for a closed surface in units of \(N - {m^2}{\text{/}}C\) are respectively \(8 \times {10^3}\) and \(4 \times {10^3}\) . Then the total charge inside the surface is [where \({\varepsilon _0} = \) permittivity constant]

1 \(4 \times {10^3}C\)
2 \( - 4 \times {10^3}C\)
3 \(\frac{{\left( { - 4 \times {{10}^3}} \right)C}}{{{\varepsilon _0}}}\)
4 \( - 4 \times {10^3}{\varepsilon _0}C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358310 If there is only one type of charge in the universe, then (\(\overrightarrow E = \) Electric field, \(d\overrightarrow S = \) Area vector)

1 \(\oint {\overrightarrow E } .d\overrightarrow S \ne 0\) on any surface
2 \(\oint {\overrightarrow E } .d\overrightarrow S \) could not be defined
3 \(\oint {\overrightarrow E } .d\overrightarrow S \ne \propto \) if charge is inside
4 \(\oint {\overrightarrow E } .d\overrightarrow S = 0\) if charge is outside, \(\frac{q}{{{\varepsilon _0}}}\) if charge is inside
PHXII01:ELECTRIC CHARGES AND FIELDS

358311 Electric flux emanating through a surface element \(d\vec S = 5\,\hat i\) placed in an electric field \(\vec E = 4\hat i + 4\hat j + 4\hat k\) is

1 10 units
2 20 units
3 4 units
4 16 units