Applications of Gauss's Law
PHXII01:ELECTRIC CHARGES AND FIELDS

357949 The adjacent diagram shows a charge +\(Q\) held on an insulating support \(S\) and enclosed by a hollow spherical conductor. \(O\) represents the centre of the spherical conductor and \(P\) is a point such that \(OP = x\,{\rm{and}}\,SP = r\). The electric field at a point \(P\) will be
supporting img

1 \(\frac{Q}{{4\pi {\varepsilon _0}{r^2}}}\)
2 \(\frac{Q}{{4\pi {\varepsilon _0}{x^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

357950 A ball having a charge \( - 100\,e\) is placed at the centre of a metallic hollow spherical shell which has a net charge of \( - 20\,e\). What is the charge on the shell's outer surface?

1 \( + 80\,e\)
2 \( - 20\,e\)
3 \( - 100\,e\)
4 \( - 120\,e\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357951 An early model for an atom considered it to have a positively charged point nucleus of charge \(Ze\), surrounded by a uniform density of negative charge upto a radius \(R\). The atom as a whole is neutral. The electric field at a distance \(r\) from the nucleus is \((r < R)\)
supporting img

1 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^2}}}} \right]\)
2 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right]\)
3 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} + \frac{1}{{{r^2}}}} \right]\)
4 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} - \frac{1}{{{r^2}}}} \right]\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357952 \({S_{1}}\) and \({S_{2}}\) are two hollow concentric spheres with charge \({q}\) and \({2 q}\). Space between \({S_{1}}\) and \({S_{2}}\) is filled with a dielectric of dielectric constants.
The ratio of flux through \({S_{2}}\) and flux through \({S_{1}}\) is \({K}\). Then, find the value of \({\dfrac{9 K}{11}}\)
supporting img

1 9
2 15
3 5
4 10
PHXII01:ELECTRIC CHARGES AND FIELDS

357953 A sphere \(S_{1}\) of radius \(R\), encloses a total charge \(q\). If there is another concentric sphere \(S_{2}\) of radius \(2 R\) and there be no additional charges between \(S_{1}\) and \(S_{2}\). What is the ratio of electric flux through \(S_{1}\) and \(S_{2}\) ?

1 1.5
2 2
3 1
4 0.5
PHXII01:ELECTRIC CHARGES AND FIELDS

357949 The adjacent diagram shows a charge +\(Q\) held on an insulating support \(S\) and enclosed by a hollow spherical conductor. \(O\) represents the centre of the spherical conductor and \(P\) is a point such that \(OP = x\,{\rm{and}}\,SP = r\). The electric field at a point \(P\) will be
supporting img

1 \(\frac{Q}{{4\pi {\varepsilon _0}{r^2}}}\)
2 \(\frac{Q}{{4\pi {\varepsilon _0}{x^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

357950 A ball having a charge \( - 100\,e\) is placed at the centre of a metallic hollow spherical shell which has a net charge of \( - 20\,e\). What is the charge on the shell's outer surface?

1 \( + 80\,e\)
2 \( - 20\,e\)
3 \( - 100\,e\)
4 \( - 120\,e\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357951 An early model for an atom considered it to have a positively charged point nucleus of charge \(Ze\), surrounded by a uniform density of negative charge upto a radius \(R\). The atom as a whole is neutral. The electric field at a distance \(r\) from the nucleus is \((r < R)\)
supporting img

1 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^2}}}} \right]\)
2 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right]\)
3 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} + \frac{1}{{{r^2}}}} \right]\)
4 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} - \frac{1}{{{r^2}}}} \right]\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357952 \({S_{1}}\) and \({S_{2}}\) are two hollow concentric spheres with charge \({q}\) and \({2 q}\). Space between \({S_{1}}\) and \({S_{2}}\) is filled with a dielectric of dielectric constants.
The ratio of flux through \({S_{2}}\) and flux through \({S_{1}}\) is \({K}\). Then, find the value of \({\dfrac{9 K}{11}}\)
supporting img

1 9
2 15
3 5
4 10
PHXII01:ELECTRIC CHARGES AND FIELDS

357953 A sphere \(S_{1}\) of radius \(R\), encloses a total charge \(q\). If there is another concentric sphere \(S_{2}\) of radius \(2 R\) and there be no additional charges between \(S_{1}\) and \(S_{2}\). What is the ratio of electric flux through \(S_{1}\) and \(S_{2}\) ?

1 1.5
2 2
3 1
4 0.5
PHXII01:ELECTRIC CHARGES AND FIELDS

357949 The adjacent diagram shows a charge +\(Q\) held on an insulating support \(S\) and enclosed by a hollow spherical conductor. \(O\) represents the centre of the spherical conductor and \(P\) is a point such that \(OP = x\,{\rm{and}}\,SP = r\). The electric field at a point \(P\) will be
supporting img

1 \(\frac{Q}{{4\pi {\varepsilon _0}{r^2}}}\)
2 \(\frac{Q}{{4\pi {\varepsilon _0}{x^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

357950 A ball having a charge \( - 100\,e\) is placed at the centre of a metallic hollow spherical shell which has a net charge of \( - 20\,e\). What is the charge on the shell's outer surface?

1 \( + 80\,e\)
2 \( - 20\,e\)
3 \( - 100\,e\)
4 \( - 120\,e\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357951 An early model for an atom considered it to have a positively charged point nucleus of charge \(Ze\), surrounded by a uniform density of negative charge upto a radius \(R\). The atom as a whole is neutral. The electric field at a distance \(r\) from the nucleus is \((r < R)\)
supporting img

1 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^2}}}} \right]\)
2 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right]\)
3 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} + \frac{1}{{{r^2}}}} \right]\)
4 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} - \frac{1}{{{r^2}}}} \right]\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357952 \({S_{1}}\) and \({S_{2}}\) are two hollow concentric spheres with charge \({q}\) and \({2 q}\). Space between \({S_{1}}\) and \({S_{2}}\) is filled with a dielectric of dielectric constants.
The ratio of flux through \({S_{2}}\) and flux through \({S_{1}}\) is \({K}\). Then, find the value of \({\dfrac{9 K}{11}}\)
supporting img

1 9
2 15
3 5
4 10
PHXII01:ELECTRIC CHARGES AND FIELDS

357953 A sphere \(S_{1}\) of radius \(R\), encloses a total charge \(q\). If there is another concentric sphere \(S_{2}\) of radius \(2 R\) and there be no additional charges between \(S_{1}\) and \(S_{2}\). What is the ratio of electric flux through \(S_{1}\) and \(S_{2}\) ?

1 1.5
2 2
3 1
4 0.5
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXII01:ELECTRIC CHARGES AND FIELDS

357949 The adjacent diagram shows a charge +\(Q\) held on an insulating support \(S\) and enclosed by a hollow spherical conductor. \(O\) represents the centre of the spherical conductor and \(P\) is a point such that \(OP = x\,{\rm{and}}\,SP = r\). The electric field at a point \(P\) will be
supporting img

1 \(\frac{Q}{{4\pi {\varepsilon _0}{r^2}}}\)
2 \(\frac{Q}{{4\pi {\varepsilon _0}{x^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

357950 A ball having a charge \( - 100\,e\) is placed at the centre of a metallic hollow spherical shell which has a net charge of \( - 20\,e\). What is the charge on the shell's outer surface?

1 \( + 80\,e\)
2 \( - 20\,e\)
3 \( - 100\,e\)
4 \( - 120\,e\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357951 An early model for an atom considered it to have a positively charged point nucleus of charge \(Ze\), surrounded by a uniform density of negative charge upto a radius \(R\). The atom as a whole is neutral. The electric field at a distance \(r\) from the nucleus is \((r < R)\)
supporting img

1 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^2}}}} \right]\)
2 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right]\)
3 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} + \frac{1}{{{r^2}}}} \right]\)
4 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} - \frac{1}{{{r^2}}}} \right]\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357952 \({S_{1}}\) and \({S_{2}}\) are two hollow concentric spheres with charge \({q}\) and \({2 q}\). Space between \({S_{1}}\) and \({S_{2}}\) is filled with a dielectric of dielectric constants.
The ratio of flux through \({S_{2}}\) and flux through \({S_{1}}\) is \({K}\). Then, find the value of \({\dfrac{9 K}{11}}\)
supporting img

1 9
2 15
3 5
4 10
PHXII01:ELECTRIC CHARGES AND FIELDS

357953 A sphere \(S_{1}\) of radius \(R\), encloses a total charge \(q\). If there is another concentric sphere \(S_{2}\) of radius \(2 R\) and there be no additional charges between \(S_{1}\) and \(S_{2}\). What is the ratio of electric flux through \(S_{1}\) and \(S_{2}\) ?

1 1.5
2 2
3 1
4 0.5
PHXII01:ELECTRIC CHARGES AND FIELDS

357949 The adjacent diagram shows a charge +\(Q\) held on an insulating support \(S\) and enclosed by a hollow spherical conductor. \(O\) represents the centre of the spherical conductor and \(P\) is a point such that \(OP = x\,{\rm{and}}\,SP = r\). The electric field at a point \(P\) will be
supporting img

1 \(\frac{Q}{{4\pi {\varepsilon _0}{r^2}}}\)
2 \(\frac{Q}{{4\pi {\varepsilon _0}{x^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

357950 A ball having a charge \( - 100\,e\) is placed at the centre of a metallic hollow spherical shell which has a net charge of \( - 20\,e\). What is the charge on the shell's outer surface?

1 \( + 80\,e\)
2 \( - 20\,e\)
3 \( - 100\,e\)
4 \( - 120\,e\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357951 An early model for an atom considered it to have a positively charged point nucleus of charge \(Ze\), surrounded by a uniform density of negative charge upto a radius \(R\). The atom as a whole is neutral. The electric field at a distance \(r\) from the nucleus is \((r < R)\)
supporting img

1 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^2}}}} \right]\)
2 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right]\)
3 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} + \frac{1}{{{r^2}}}} \right]\)
4 \(\frac{{Ze}}{{4\pi {\varepsilon _0}}}\left[ {\frac{r}{{{R^3}}} - \frac{1}{{{r^2}}}} \right]\)
PHXII01:ELECTRIC CHARGES AND FIELDS

357952 \({S_{1}}\) and \({S_{2}}\) are two hollow concentric spheres with charge \({q}\) and \({2 q}\). Space between \({S_{1}}\) and \({S_{2}}\) is filled with a dielectric of dielectric constants.
The ratio of flux through \({S_{2}}\) and flux through \({S_{1}}\) is \({K}\). Then, find the value of \({\dfrac{9 K}{11}}\)
supporting img

1 9
2 15
3 5
4 10
PHXII01:ELECTRIC CHARGES AND FIELDS

357953 A sphere \(S_{1}\) of radius \(R\), encloses a total charge \(q\). If there is another concentric sphere \(S_{2}\) of radius \(2 R\) and there be no additional charges between \(S_{1}\) and \(S_{2}\). What is the ratio of electric flux through \(S_{1}\) and \(S_{2}\) ?

1 1.5
2 2
3 1
4 0.5