Relation between Field and Potential
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359541 In uniform electric field \({\vec{E}=10 {~N} / {C}}\) as shown in the figure. The value of \({\left(V_{A}-V_{B}\right)}\) is
supporting img

1 \({10 V}\)
2 \({-10 V}\)
3 \({20 V}\)
4 \({-20 V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359542 The potential at a point \(x\) (measured in \(\mu \) \(m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = \frac{{20}}{{{x^2} - 4}}\) volt. The electric field \(E\) at \(x = 4\,\mu \) \(m\) is given by

1 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the positive \(x\) - direction
2 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the negative \(x\) - direction
3 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the positive \(x\)-direction
4 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the negative direction
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359543 The electric potential \(V\) at any point \(({\rm{x}},y,z)\), all in metres in space is given by \(V = 4{x^2}\) volt. The electric field at the point (1, 0, 2) in volt/meter, is

1 8 along positive \(X\)-axis
2 8 along negative \(X\)-axis
3 16 along negative \(X\)-axis
4 16 along positive \(X\)-axis
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359544 The electric field \({\vec{E}}\) between two points is constant in both magnitude and direction. Consider a path of length \({d}\) at an angle \({\theta=60^{\circ}}\) with respect to field lines shown in the figure. The potential difference between points 1 and 2 is
supporting img

1 \({\dfrac{E}{d \cos 60^{\circ}}}\)
2 \({E d \cos 60^{\circ}}\)
3 \({\dfrac{E d}{\cos 60^{\circ}}}\)
4 \({\dfrac{E}{d} \cos 60^{\circ}}\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359541 In uniform electric field \({\vec{E}=10 {~N} / {C}}\) as shown in the figure. The value of \({\left(V_{A}-V_{B}\right)}\) is
supporting img

1 \({10 V}\)
2 \({-10 V}\)
3 \({20 V}\)
4 \({-20 V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359542 The potential at a point \(x\) (measured in \(\mu \) \(m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = \frac{{20}}{{{x^2} - 4}}\) volt. The electric field \(E\) at \(x = 4\,\mu \) \(m\) is given by

1 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the positive \(x\) - direction
2 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the negative \(x\) - direction
3 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the positive \(x\)-direction
4 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the negative direction
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359543 The electric potential \(V\) at any point \(({\rm{x}},y,z)\), all in metres in space is given by \(V = 4{x^2}\) volt. The electric field at the point (1, 0, 2) in volt/meter, is

1 8 along positive \(X\)-axis
2 8 along negative \(X\)-axis
3 16 along negative \(X\)-axis
4 16 along positive \(X\)-axis
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359544 The electric field \({\vec{E}}\) between two points is constant in both magnitude and direction. Consider a path of length \({d}\) at an angle \({\theta=60^{\circ}}\) with respect to field lines shown in the figure. The potential difference between points 1 and 2 is
supporting img

1 \({\dfrac{E}{d \cos 60^{\circ}}}\)
2 \({E d \cos 60^{\circ}}\)
3 \({\dfrac{E d}{\cos 60^{\circ}}}\)
4 \({\dfrac{E}{d} \cos 60^{\circ}}\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359541 In uniform electric field \({\vec{E}=10 {~N} / {C}}\) as shown in the figure. The value of \({\left(V_{A}-V_{B}\right)}\) is
supporting img

1 \({10 V}\)
2 \({-10 V}\)
3 \({20 V}\)
4 \({-20 V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359542 The potential at a point \(x\) (measured in \(\mu \) \(m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = \frac{{20}}{{{x^2} - 4}}\) volt. The electric field \(E\) at \(x = 4\,\mu \) \(m\) is given by

1 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the positive \(x\) - direction
2 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the negative \(x\) - direction
3 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the positive \(x\)-direction
4 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the negative direction
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359543 The electric potential \(V\) at any point \(({\rm{x}},y,z)\), all in metres in space is given by \(V = 4{x^2}\) volt. The electric field at the point (1, 0, 2) in volt/meter, is

1 8 along positive \(X\)-axis
2 8 along negative \(X\)-axis
3 16 along negative \(X\)-axis
4 16 along positive \(X\)-axis
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359544 The electric field \({\vec{E}}\) between two points is constant in both magnitude and direction. Consider a path of length \({d}\) at an angle \({\theta=60^{\circ}}\) with respect to field lines shown in the figure. The potential difference between points 1 and 2 is
supporting img

1 \({\dfrac{E}{d \cos 60^{\circ}}}\)
2 \({E d \cos 60^{\circ}}\)
3 \({\dfrac{E d}{\cos 60^{\circ}}}\)
4 \({\dfrac{E}{d} \cos 60^{\circ}}\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359541 In uniform electric field \({\vec{E}=10 {~N} / {C}}\) as shown in the figure. The value of \({\left(V_{A}-V_{B}\right)}\) is
supporting img

1 \({10 V}\)
2 \({-10 V}\)
3 \({20 V}\)
4 \({-20 V}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359542 The potential at a point \(x\) (measured in \(\mu \) \(m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = \frac{{20}}{{{x^2} - 4}}\) volt. The electric field \(E\) at \(x = 4\,\mu \) \(m\) is given by

1 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the positive \(x\) - direction
2 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the negative \(x\) - direction
3 \(\frac{{10}}{9}\frac{V}{{\mu m}}\) and in the positive \(x\)-direction
4 \(\frac{5}{3}\frac{V}{{\mu m}}\) and in the negative direction
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359543 The electric potential \(V\) at any point \(({\rm{x}},y,z)\), all in metres in space is given by \(V = 4{x^2}\) volt. The electric field at the point (1, 0, 2) in volt/meter, is

1 8 along positive \(X\)-axis
2 8 along negative \(X\)-axis
3 16 along negative \(X\)-axis
4 16 along positive \(X\)-axis
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359544 The electric field \({\vec{E}}\) between two points is constant in both magnitude and direction. Consider a path of length \({d}\) at an angle \({\theta=60^{\circ}}\) with respect to field lines shown in the figure. The potential difference between points 1 and 2 is
supporting img

1 \({\dfrac{E}{d \cos 60^{\circ}}}\)
2 \({E d \cos 60^{\circ}}\)
3 \({\dfrac{E d}{\cos 60^{\circ}}}\)
4 \({\dfrac{E}{d} \cos 60^{\circ}}\)
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