Electric potential and electrostatic energy

Compute the electric potential at $15\mathrm{cm}$ from a point charge $Q=-3.0\mathrm{nC}$, with zero potential at infinite distance.

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In a uniform electric field of magnitude $E=1.2\cdot 10^{4}V/m$ a charge $q=5.0\mu \mathrm{C}$ moves $8.0\mathrm{cm}$ in the direction opposite to the field. Compute the work done by the electric force.

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An electron starts from rest and crosses a potential difference of $250\mathrm{V}$. Compute its final speed, neglecting the weight.

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A proton, of mass $m_p=1.67\cdot 10^{-27}\mathrm{kg}$, has kinetic energy $2.0\mathrm{keV}$. Express the energy in joules and compute the speed of the proton.

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Two point charges $q_1=+5.0\mu \mathrm{C}$ and $q_2=-2.0\mu \mathrm{C}$ are at rest at a distance of $30\mathrm{cm}$. Compute the external work needed to bring them slowly to infinite distance from each other.

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A dipole has moment $p=4.0\cdot 10^{-12}\mathrm{C}\cdot \mathrm{m}$. Compute the potential at a point $5.0\mathrm{cm}$ from the center of the dipole, much greater than the distance between the charges, in a direction that makes an angle of $60^{\circ }$ with the dipole moment.

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A thin ring of radius $5.0\mathrm{cm}$ carries the charge $10\mathrm{nC}$ distributed uniformly. Compute the potential at the point of the axis $12\mathrm{cm}$ from the center.

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An insulating sphere of radius $5.0\mathrm{cm}$ carries the charge $2.0\mathrm{nC}$ distributed uniformly throughout its volume. Compute the potential at the center of the sphere.

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In a charge-free region the potential is $V(x,y)=a(3x^{2}y-y^3)$, with $a=20V/{\mathrm{m}}^3$. Compute the electric field at the point $(1.0,1.0)\mathrm{m}$.

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The charges $+q$, $+q$ and $-2q$, with $q=1.0\mu \mathrm{C}$, occupy the vertices of an equilateral triangle of side $15\mathrm{cm}$. Compute the electrostatic energy of the system.

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A proton with kinetic energy $1.2\mathrm{MeV}$, very far from an iron nucleus of charge $26e$, moves head-on toward the nucleus, considered at rest. Compute the distance of closest approach.

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A very long straight wire carries the uniform charge $\lambda =2.0nC/m$. Compute the difference between the potential at $2.0\mathrm{cm}$ and the potential at $8.0\mathrm{cm}$ from the wire.

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In a region with a uniform field the equipotential surfaces are parallel planes; two consecutive planes are $5.0\mathrm{mm}$ apart and their potentials differ by $20\mathrm{V}$. Compute the magnitude of the field and the work done by the field on an electron that goes from the surface at $10\mathrm{V}$ to the surface at $50\mathrm{V}$.

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