Relation between Field and Potential
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359554 An electron enters between two horizontal plates separated by 2 \(mm\) and having a potential difference of 1000 \(V\). The force on electron is

1 \(8 \times {10^{ - 9}}N\)
2 \(8 \times {10^{ - 12}}N\)
3 \(8 \times {10^{14}}N\)
4 \(8 \times {10^{ - 14}}N\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359555 A hollow charged metal sphere has radius \({r}\). If the potential difference between its surface and a point at distance \({3 r}\) from the centre is \({V}\), then the electric intensity at distance \({3 r}\) from the centre is

1 \({\dfrac{V}{6 r}}\)
2 \({\dfrac{V}{4 r}}\)
3 \({\dfrac{V}{3 r}}\)
4 \({\dfrac{V}{2 r}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359556 Potential difference is given as
\(V(x)=-x^{2} y\) volt. Find electric field at
a point \((1,2)\).

1 \(\hat i + 4\hat jV{\text{ }}{m^{ - 1}}\)
2 \( - 4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
3 \(4\widehat i + \widehat j{\text{ }}V{m^{ - 1}}\)
4 \(4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359557 The electric potential at a point (x,y,z) is given by \(V = - {x^2}y - x{z^3} + 4\) The electric field \(E\) at the point is

1 \(E = (2xy + {z^3})\hat i + {x^2}\hat j + 3x{z^2}\hat k\)
2 \(E = (2xy - {z^3})\hat i + x{y^2}\hat j + 3{z^2}x\hat k\)
3 \(E = 2xy\hat i + ({x^2} + {y^2})\hat j + (3xz - {y^2})\hat k\)
4 \(E = {z^3}\hat i + xyz\hat j + {z^2}\hat k\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359554 An electron enters between two horizontal plates separated by 2 \(mm\) and having a potential difference of 1000 \(V\). The force on electron is

1 \(8 \times {10^{ - 9}}N\)
2 \(8 \times {10^{ - 12}}N\)
3 \(8 \times {10^{14}}N\)
4 \(8 \times {10^{ - 14}}N\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359555 A hollow charged metal sphere has radius \({r}\). If the potential difference between its surface and a point at distance \({3 r}\) from the centre is \({V}\), then the electric intensity at distance \({3 r}\) from the centre is

1 \({\dfrac{V}{6 r}}\)
2 \({\dfrac{V}{4 r}}\)
3 \({\dfrac{V}{3 r}}\)
4 \({\dfrac{V}{2 r}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359556 Potential difference is given as
\(V(x)=-x^{2} y\) volt. Find electric field at
a point \((1,2)\).

1 \(\hat i + 4\hat jV{\text{ }}{m^{ - 1}}\)
2 \( - 4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
3 \(4\widehat i + \widehat j{\text{ }}V{m^{ - 1}}\)
4 \(4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359557 The electric potential at a point (x,y,z) is given by \(V = - {x^2}y - x{z^3} + 4\) The electric field \(E\) at the point is

1 \(E = (2xy + {z^3})\hat i + {x^2}\hat j + 3x{z^2}\hat k\)
2 \(E = (2xy - {z^3})\hat i + x{y^2}\hat j + 3{z^2}x\hat k\)
3 \(E = 2xy\hat i + ({x^2} + {y^2})\hat j + (3xz - {y^2})\hat k\)
4 \(E = {z^3}\hat i + xyz\hat j + {z^2}\hat k\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359554 An electron enters between two horizontal plates separated by 2 \(mm\) and having a potential difference of 1000 \(V\). The force on electron is

1 \(8 \times {10^{ - 9}}N\)
2 \(8 \times {10^{ - 12}}N\)
3 \(8 \times {10^{14}}N\)
4 \(8 \times {10^{ - 14}}N\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359555 A hollow charged metal sphere has radius \({r}\). If the potential difference between its surface and a point at distance \({3 r}\) from the centre is \({V}\), then the electric intensity at distance \({3 r}\) from the centre is

1 \({\dfrac{V}{6 r}}\)
2 \({\dfrac{V}{4 r}}\)
3 \({\dfrac{V}{3 r}}\)
4 \({\dfrac{V}{2 r}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359556 Potential difference is given as
\(V(x)=-x^{2} y\) volt. Find electric field at
a point \((1,2)\).

1 \(\hat i + 4\hat jV{\text{ }}{m^{ - 1}}\)
2 \( - 4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
3 \(4\widehat i + \widehat j{\text{ }}V{m^{ - 1}}\)
4 \(4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359557 The electric potential at a point (x,y,z) is given by \(V = - {x^2}y - x{z^3} + 4\) The electric field \(E\) at the point is

1 \(E = (2xy + {z^3})\hat i + {x^2}\hat j + 3x{z^2}\hat k\)
2 \(E = (2xy - {z^3})\hat i + x{y^2}\hat j + 3{z^2}x\hat k\)
3 \(E = 2xy\hat i + ({x^2} + {y^2})\hat j + (3xz - {y^2})\hat k\)
4 \(E = {z^3}\hat i + xyz\hat j + {z^2}\hat k\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359554 An electron enters between two horizontal plates separated by 2 \(mm\) and having a potential difference of 1000 \(V\). The force on electron is

1 \(8 \times {10^{ - 9}}N\)
2 \(8 \times {10^{ - 12}}N\)
3 \(8 \times {10^{14}}N\)
4 \(8 \times {10^{ - 14}}N\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359555 A hollow charged metal sphere has radius \({r}\). If the potential difference between its surface and a point at distance \({3 r}\) from the centre is \({V}\), then the electric intensity at distance \({3 r}\) from the centre is

1 \({\dfrac{V}{6 r}}\)
2 \({\dfrac{V}{4 r}}\)
3 \({\dfrac{V}{3 r}}\)
4 \({\dfrac{V}{2 r}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359556 Potential difference is given as
\(V(x)=-x^{2} y\) volt. Find electric field at
a point \((1,2)\).

1 \(\hat i + 4\hat jV{\text{ }}{m^{ - 1}}\)
2 \( - 4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
3 \(4\widehat i + \widehat j{\text{ }}V{m^{ - 1}}\)
4 \(4\widehat i - \widehat j{\text{ }}V{m^{ - 1}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359557 The electric potential at a point (x,y,z) is given by \(V = - {x^2}y - x{z^3} + 4\) The electric field \(E\) at the point is

1 \(E = (2xy + {z^3})\hat i + {x^2}\hat j + 3x{z^2}\hat k\)
2 \(E = (2xy - {z^3})\hat i + x{y^2}\hat j + 3{z^2}x\hat k\)
3 \(E = 2xy\hat i + ({x^2} + {y^2})\hat j + (3xz - {y^2})\hat k\)
4 \(E = {z^3}\hat i + xyz\hat j + {z^2}\hat k\)
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