Continuous Charge Distribution
PHXII01:ELECTRIC CHARGES AND FIELDS

358015 A positively charged sphere of radius \({r_0}\) carries a volume charge density \(\rho \). A spherical cavity of radius \({r_0}/2\) is then scooped out and left empty.\({C_1}\) is the centre of the sphere and \({C_2}\) that of the cavity. What is the direction and magnitude of the electric field at point \(B\)?
supporting img

1 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}left\)
2 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}left\)
3 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}right\)
4 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}right\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358016 A conducting sphere of radius \(20\,cm\) has a known charge. If the electric field at a distance \(40\,cm\) from the centre of the sphere is \(1.2 \times {10^3}\,N{C^{ - 1}}\) and points radially inwards. The net charge on the sphere is:

1 \( - 4.5 \times {10^{ - 9}}\,C\)
2 \( 4.5 \times {10^{9}}\,C\)
3 \( - 21.3 \times {10^{ - 9}}\,C\)
4 \( 21.3 \times {10^{9}}\,C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358017 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
supporting img

1 Zero everywhere
2 Uniform
3 Non-uniform
4 Zero only at its center
PHXII01:ELECTRIC CHARGES AND FIELDS

358018 \(4 \times {10^{10}}\) electrons are removed from a neutral metal sphere of diameter \(20\,cm\) placed in air. The magnitude of the electric field (in \(N{C^{ - 1}}\)) at a distance of 20 \(cm\) from its centre is

1 \({\rm{zero}}\)
2 \({\rm{5760}}\)
3 \({\rm{640}}\)
4 \({\rm{1440}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358019 \(\sigma \) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is

1 \(\sigma / \varepsilon_{0}\)
2 \(\sigma / 4 \varepsilon_{0}\)
3 \(\sigma / \varepsilon_{0} R\)
4 \(\sigma / 2 \varepsilon_{0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358015 A positively charged sphere of radius \({r_0}\) carries a volume charge density \(\rho \). A spherical cavity of radius \({r_0}/2\) is then scooped out and left empty.\({C_1}\) is the centre of the sphere and \({C_2}\) that of the cavity. What is the direction and magnitude of the electric field at point \(B\)?
supporting img

1 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}left\)
2 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}left\)
3 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}right\)
4 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}right\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358016 A conducting sphere of radius \(20\,cm\) has a known charge. If the electric field at a distance \(40\,cm\) from the centre of the sphere is \(1.2 \times {10^3}\,N{C^{ - 1}}\) and points radially inwards. The net charge on the sphere is:

1 \( - 4.5 \times {10^{ - 9}}\,C\)
2 \( 4.5 \times {10^{9}}\,C\)
3 \( - 21.3 \times {10^{ - 9}}\,C\)
4 \( 21.3 \times {10^{9}}\,C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358017 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
supporting img

1 Zero everywhere
2 Uniform
3 Non-uniform
4 Zero only at its center
PHXII01:ELECTRIC CHARGES AND FIELDS

358018 \(4 \times {10^{10}}\) electrons are removed from a neutral metal sphere of diameter \(20\,cm\) placed in air. The magnitude of the electric field (in \(N{C^{ - 1}}\)) at a distance of 20 \(cm\) from its centre is

1 \({\rm{zero}}\)
2 \({\rm{5760}}\)
3 \({\rm{640}}\)
4 \({\rm{1440}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358019 \(\sigma \) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is

1 \(\sigma / \varepsilon_{0}\)
2 \(\sigma / 4 \varepsilon_{0}\)
3 \(\sigma / \varepsilon_{0} R\)
4 \(\sigma / 2 \varepsilon_{0}\)
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PHXII01:ELECTRIC CHARGES AND FIELDS

358015 A positively charged sphere of radius \({r_0}\) carries a volume charge density \(\rho \). A spherical cavity of radius \({r_0}/2\) is then scooped out and left empty.\({C_1}\) is the centre of the sphere and \({C_2}\) that of the cavity. What is the direction and magnitude of the electric field at point \(B\)?
supporting img

1 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}left\)
2 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}left\)
3 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}right\)
4 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}right\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358016 A conducting sphere of radius \(20\,cm\) has a known charge. If the electric field at a distance \(40\,cm\) from the centre of the sphere is \(1.2 \times {10^3}\,N{C^{ - 1}}\) and points radially inwards. The net charge on the sphere is:

1 \( - 4.5 \times {10^{ - 9}}\,C\)
2 \( 4.5 \times {10^{9}}\,C\)
3 \( - 21.3 \times {10^{ - 9}}\,C\)
4 \( 21.3 \times {10^{9}}\,C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358017 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
supporting img

1 Zero everywhere
2 Uniform
3 Non-uniform
4 Zero only at its center
PHXII01:ELECTRIC CHARGES AND FIELDS

358018 \(4 \times {10^{10}}\) electrons are removed from a neutral metal sphere of diameter \(20\,cm\) placed in air. The magnitude of the electric field (in \(N{C^{ - 1}}\)) at a distance of 20 \(cm\) from its centre is

1 \({\rm{zero}}\)
2 \({\rm{5760}}\)
3 \({\rm{640}}\)
4 \({\rm{1440}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358019 \(\sigma \) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is

1 \(\sigma / \varepsilon_{0}\)
2 \(\sigma / 4 \varepsilon_{0}\)
3 \(\sigma / \varepsilon_{0} R\)
4 \(\sigma / 2 \varepsilon_{0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358015 A positively charged sphere of radius \({r_0}\) carries a volume charge density \(\rho \). A spherical cavity of radius \({r_0}/2\) is then scooped out and left empty.\({C_1}\) is the centre of the sphere and \({C_2}\) that of the cavity. What is the direction and magnitude of the electric field at point \(B\)?
supporting img

1 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}left\)
2 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}left\)
3 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}right\)
4 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}right\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358016 A conducting sphere of radius \(20\,cm\) has a known charge. If the electric field at a distance \(40\,cm\) from the centre of the sphere is \(1.2 \times {10^3}\,N{C^{ - 1}}\) and points radially inwards. The net charge on the sphere is:

1 \( - 4.5 \times {10^{ - 9}}\,C\)
2 \( 4.5 \times {10^{9}}\,C\)
3 \( - 21.3 \times {10^{ - 9}}\,C\)
4 \( 21.3 \times {10^{9}}\,C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358017 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
supporting img

1 Zero everywhere
2 Uniform
3 Non-uniform
4 Zero only at its center
PHXII01:ELECTRIC CHARGES AND FIELDS

358018 \(4 \times {10^{10}}\) electrons are removed from a neutral metal sphere of diameter \(20\,cm\) placed in air. The magnitude of the electric field (in \(N{C^{ - 1}}\)) at a distance of 20 \(cm\) from its centre is

1 \({\rm{zero}}\)
2 \({\rm{5760}}\)
3 \({\rm{640}}\)
4 \({\rm{1440}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358019 \(\sigma \) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is

1 \(\sigma / \varepsilon_{0}\)
2 \(\sigma / 4 \varepsilon_{0}\)
3 \(\sigma / \varepsilon_{0} R\)
4 \(\sigma / 2 \varepsilon_{0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358015 A positively charged sphere of radius \({r_0}\) carries a volume charge density \(\rho \). A spherical cavity of radius \({r_0}/2\) is then scooped out and left empty.\({C_1}\) is the centre of the sphere and \({C_2}\) that of the cavity. What is the direction and magnitude of the electric field at point \(B\)?
supporting img

1 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}left\)
2 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}left\)
3 \(\frac{{17\rho {r_0}}}{{54{\varepsilon _0}}}right\)
4 \(\frac{{\rho {r_0}}}{{6{\varepsilon _0}}}right\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358016 A conducting sphere of radius \(20\,cm\) has a known charge. If the electric field at a distance \(40\,cm\) from the centre of the sphere is \(1.2 \times {10^3}\,N{C^{ - 1}}\) and points radially inwards. The net charge on the sphere is:

1 \( - 4.5 \times {10^{ - 9}}\,C\)
2 \( 4.5 \times {10^{9}}\,C\)
3 \( - 21.3 \times {10^{ - 9}}\,C\)
4 \( 21.3 \times {10^{9}}\,C\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358017 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
supporting img

1 Zero everywhere
2 Uniform
3 Non-uniform
4 Zero only at its center
PHXII01:ELECTRIC CHARGES AND FIELDS

358018 \(4 \times {10^{10}}\) electrons are removed from a neutral metal sphere of diameter \(20\,cm\) placed in air. The magnitude of the electric field (in \(N{C^{ - 1}}\)) at a distance of 20 \(cm\) from its centre is

1 \({\rm{zero}}\)
2 \({\rm{5760}}\)
3 \({\rm{640}}\)
4 \({\rm{1440}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358019 \(\sigma \) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is

1 \(\sigma / \varepsilon_{0}\)
2 \(\sigma / 4 \varepsilon_{0}\)
3 \(\sigma / \varepsilon_{0} R\)
4 \(\sigma / 2 \varepsilon_{0}\)