GAUSS’S LAW
Electric Charges and Fields

272195 A long cylindrical volume contains a uniformly distributed charge of density $\rho $. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

1 $\frac{\rho q{{R}^{2}}}{4{{\varepsilon }_{0}}}$
2 $\frac{\rho q{{R}^{2}}}{2{{\varepsilon }_{0}}}$
3 $\frac{q\rho }{4{{\varepsilon }_{0}}{{R}^{2}}}$
4 $\frac{4{{\varepsilon }_{0}}{{R}^{2}}}{q\rho }$
Electric Charges and Fields

272196 A solid conducting sphere of radius a has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$.The surface charge density on the inner and outer surfaces of the spherical shell will be

1 $-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
2 $-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
3 $0,\frac{Q}{4\pi {{c}^{2}}}$
4 None of the above
Electric Charges and Fields

272197 If electric field in a region is radially outward with magnitude $E=Ar$, the charge contained in a sphere of radius $r$ centred at the origin is

1 $\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}$
2 $4\pi {{\varepsilon }_{0}}A{{r}^{3}}$
3 $\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}$
4 $\frac{4\pi {{\varepsilon }_{0}}~A}{{{r}^{3}}}$
Electric Charges and Fields

272198 Let $\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point ' $P$ ' inside the sphere at distance ${{r}_{1}}$ from the centre of the sphere, the magnitude of electric field is :

1 $\frac{Q}{4\pi {{\epsilon }_{0}}r_{1}^{2}}$
2 $\frac{Qr_{1}^{2}}{4\pi {{\epsilon }_{0}}{{R}^{4}}}$
3 $\frac{Q{{r}_{1}}{{~}^{2}}}{3\pi {{\epsilon }_{0}}{{R}^{4}}}$
4 0
Electric Charges and Fields

272199 The Gaussian surface

1 can pass through a continuous charge distribution.
2 cannot pass through a continuous charge distribution.
3 can pass through any system of discrete charges.
4 can pass through a continuous charge distribution as well as any system of discrete charges.
Electric Charges and Fields

272195 A long cylindrical volume contains a uniformly distributed charge of density $\rho $. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

1 $\frac{\rho q{{R}^{2}}}{4{{\varepsilon }_{0}}}$
2 $\frac{\rho q{{R}^{2}}}{2{{\varepsilon }_{0}}}$
3 $\frac{q\rho }{4{{\varepsilon }_{0}}{{R}^{2}}}$
4 $\frac{4{{\varepsilon }_{0}}{{R}^{2}}}{q\rho }$
Electric Charges and Fields

272196 A solid conducting sphere of radius a has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$.The surface charge density on the inner and outer surfaces of the spherical shell will be

1 $-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
2 $-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
3 $0,\frac{Q}{4\pi {{c}^{2}}}$
4 None of the above
Electric Charges and Fields

272197 If electric field in a region is radially outward with magnitude $E=Ar$, the charge contained in a sphere of radius $r$ centred at the origin is

1 $\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}$
2 $4\pi {{\varepsilon }_{0}}A{{r}^{3}}$
3 $\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}$
4 $\frac{4\pi {{\varepsilon }_{0}}~A}{{{r}^{3}}}$
Electric Charges and Fields

272198 Let $\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point ' $P$ ' inside the sphere at distance ${{r}_{1}}$ from the centre of the sphere, the magnitude of electric field is :

1 $\frac{Q}{4\pi {{\epsilon }_{0}}r_{1}^{2}}$
2 $\frac{Qr_{1}^{2}}{4\pi {{\epsilon }_{0}}{{R}^{4}}}$
3 $\frac{Q{{r}_{1}}{{~}^{2}}}{3\pi {{\epsilon }_{0}}{{R}^{4}}}$
4 0
Electric Charges and Fields

272199 The Gaussian surface

1 can pass through a continuous charge distribution.
2 cannot pass through a continuous charge distribution.
3 can pass through any system of discrete charges.
4 can pass through a continuous charge distribution as well as any system of discrete charges.
Electric Charges and Fields

272195 A long cylindrical volume contains a uniformly distributed charge of density $\rho $. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

1 $\frac{\rho q{{R}^{2}}}{4{{\varepsilon }_{0}}}$
2 $\frac{\rho q{{R}^{2}}}{2{{\varepsilon }_{0}}}$
3 $\frac{q\rho }{4{{\varepsilon }_{0}}{{R}^{2}}}$
4 $\frac{4{{\varepsilon }_{0}}{{R}^{2}}}{q\rho }$
Electric Charges and Fields

272196 A solid conducting sphere of radius a has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$.The surface charge density on the inner and outer surfaces of the spherical shell will be

1 $-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
2 $-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
3 $0,\frac{Q}{4\pi {{c}^{2}}}$
4 None of the above
Electric Charges and Fields

272197 If electric field in a region is radially outward with magnitude $E=Ar$, the charge contained in a sphere of radius $r$ centred at the origin is

1 $\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}$
2 $4\pi {{\varepsilon }_{0}}A{{r}^{3}}$
3 $\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}$
4 $\frac{4\pi {{\varepsilon }_{0}}~A}{{{r}^{3}}}$
Electric Charges and Fields

272198 Let $\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point ' $P$ ' inside the sphere at distance ${{r}_{1}}$ from the centre of the sphere, the magnitude of electric field is :

1 $\frac{Q}{4\pi {{\epsilon }_{0}}r_{1}^{2}}$
2 $\frac{Qr_{1}^{2}}{4\pi {{\epsilon }_{0}}{{R}^{4}}}$
3 $\frac{Q{{r}_{1}}{{~}^{2}}}{3\pi {{\epsilon }_{0}}{{R}^{4}}}$
4 0
Electric Charges and Fields

272199 The Gaussian surface

1 can pass through a continuous charge distribution.
2 cannot pass through a continuous charge distribution.
3 can pass through any system of discrete charges.
4 can pass through a continuous charge distribution as well as any system of discrete charges.
Electric Charges and Fields

272195 A long cylindrical volume contains a uniformly distributed charge of density $\rho $. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

1 $\frac{\rho q{{R}^{2}}}{4{{\varepsilon }_{0}}}$
2 $\frac{\rho q{{R}^{2}}}{2{{\varepsilon }_{0}}}$
3 $\frac{q\rho }{4{{\varepsilon }_{0}}{{R}^{2}}}$
4 $\frac{4{{\varepsilon }_{0}}{{R}^{2}}}{q\rho }$
Electric Charges and Fields

272196 A solid conducting sphere of radius a has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$.The surface charge density on the inner and outer surfaces of the spherical shell will be

1 $-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
2 $-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
3 $0,\frac{Q}{4\pi {{c}^{2}}}$
4 None of the above
Electric Charges and Fields

272197 If electric field in a region is radially outward with magnitude $E=Ar$, the charge contained in a sphere of radius $r$ centred at the origin is

1 $\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}$
2 $4\pi {{\varepsilon }_{0}}A{{r}^{3}}$
3 $\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}$
4 $\frac{4\pi {{\varepsilon }_{0}}~A}{{{r}^{3}}}$
Electric Charges and Fields

272198 Let $\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point ' $P$ ' inside the sphere at distance ${{r}_{1}}$ from the centre of the sphere, the magnitude of electric field is :

1 $\frac{Q}{4\pi {{\epsilon }_{0}}r_{1}^{2}}$
2 $\frac{Qr_{1}^{2}}{4\pi {{\epsilon }_{0}}{{R}^{4}}}$
3 $\frac{Q{{r}_{1}}{{~}^{2}}}{3\pi {{\epsilon }_{0}}{{R}^{4}}}$
4 0
Electric Charges and Fields

272199 The Gaussian surface

1 can pass through a continuous charge distribution.
2 cannot pass through a continuous charge distribution.
3 can pass through any system of discrete charges.
4 can pass through a continuous charge distribution as well as any system of discrete charges.
Electric Charges and Fields

272195 A long cylindrical volume contains a uniformly distributed charge of density $\rho $. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

1 $\frac{\rho q{{R}^{2}}}{4{{\varepsilon }_{0}}}$
2 $\frac{\rho q{{R}^{2}}}{2{{\varepsilon }_{0}}}$
3 $\frac{q\rho }{4{{\varepsilon }_{0}}{{R}^{2}}}$
4 $\frac{4{{\varepsilon }_{0}}{{R}^{2}}}{q\rho }$
Electric Charges and Fields

272196 A solid conducting sphere of radius a has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$.The surface charge density on the inner and outer surfaces of the spherical shell will be

1 $-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
2 $-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}$
3 $0,\frac{Q}{4\pi {{c}^{2}}}$
4 None of the above
Electric Charges and Fields

272197 If electric field in a region is radially outward with magnitude $E=Ar$, the charge contained in a sphere of radius $r$ centred at the origin is

1 $\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}$
2 $4\pi {{\varepsilon }_{0}}A{{r}^{3}}$
3 $\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}$
4 $\frac{4\pi {{\varepsilon }_{0}}~A}{{{r}^{3}}}$
Electric Charges and Fields

272198 Let $\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point ' $P$ ' inside the sphere at distance ${{r}_{1}}$ from the centre of the sphere, the magnitude of electric field is :

1 $\frac{Q}{4\pi {{\epsilon }_{0}}r_{1}^{2}}$
2 $\frac{Qr_{1}^{2}}{4\pi {{\epsilon }_{0}}{{R}^{4}}}$
3 $\frac{Q{{r}_{1}}{{~}^{2}}}{3\pi {{\epsilon }_{0}}{{R}^{4}}}$
4 0
Electric Charges and Fields

272199 The Gaussian surface

1 can pass through a continuous charge distribution.
2 cannot pass through a continuous charge distribution.
3 can pass through any system of discrete charges.
4 can pass through a continuous charge distribution as well as any system of discrete charges.