Electric charge and Coulomb’s law

A plastic rod rubbed with a wool cloth acquires the charge $q=-4.0\mathrm{nC}$. Compute the number of electrons that the rod received from the cloth and the final charge of the cloth, assuming that both were initially neutral.

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Two point charges $q_1=+5.0\mathrm{nC}$ and $q_2=-8.0\mathrm{nC}$ are in vacuum at distance $4.0\mathrm{cm}$. Compute the magnitude of the force between the two charges and determine whether it is attractive or repulsive.

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Two equal point charges of $1.0\mu \mathrm{C}$ repel each other in vacuum with a force of magnitude $1.0\mathrm{N}$. Compute their distance.

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Two protons in an atomic nucleus are $2.0\cdot 10^{-15}\mathrm{m}$ apart. Compute the magnitude of the electric force between the two protons and the ratio between the electric force and the gravitational force, with $G=6.67\cdot 10^{-11}\mathrm{N}\cdot {\mathrm{m}}^2/k{\mathrm{g}}^2$ and proton mass $m_p=1.67\cdot 10^{-27}\mathrm{kg}$.

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Two identical conducting spheres $A$ and $B$ have charges $q_A=+7.0\mathrm{nC}$ and $q_B=-3.0\mathrm{nC}$. The spheres are brought into contact and then separated. Compute the final charge of each sphere and the number of electrons that pass from one sphere to the other, indicating the direction.

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Two point charges attract each other with a force of magnitude $F$. One of the two charges is halved and the distance is doubled. Express the magnitude of the new force in terms of $F$.

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On the $x$-axis, in vacuum, there are the point charges $q_1=+5.0\mu \mathrm{C}$ at $x=0$ and $q_2=+5.0\mu \mathrm{C}$ at $x=0.40\mathrm{m}$. Compute the magnitude and orientation of the total force on the charge $q_0=-1.0\mu \mathrm{C}$ placed at $x=0.10\mathrm{m}$.

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In vacuum the charge $q_0=+1.0\mu \mathrm{C}$ is at the origin, and two equal charges $q=-2.0\mu \mathrm{C}$ are at the points $(0.20\mathrm{m};0)$ and $(0;0.20\mathrm{m})$. Compute the magnitude and direction of the total force on $q_0$.

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Two point charges $q_1=+1.0\mathrm{nC}$ and $q_2=+9.0\mathrm{nC}$ are fixed in vacuum at $x=0$ and at $x=0.40\mathrm{m}$. Determine the point at which a third charge, subject only to the forces of $q_1$ and $q_2$, is in equilibrium.

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Two point charges $q_1=-2.0\mu \mathrm{C}$ and $q_2=+8.0\mu \mathrm{C}$ are fixed in vacuum at $x=0$ and at $x=0.30\mathrm{m}$. Determine the point of the $x$-axis at which a third charge is in equilibrium.

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Two identical small spheres of mass $2.0\mathrm{g}$, with the same charge, hang from the same point on two insulating strings $30\mathrm{cm}$ long. At equilibrium each string forms an angle of $15^{\circ }$ with the vertical. Compute the absolute value of the charge of each sphere.

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A small sphere of mass $0.50\mathrm{g}$ and charge $+20\mathrm{nC}$ can slide without friction in a vertical insulating tube, at the bottom of which the point charge $+50\mathrm{nC}$ is fixed. Compute the distance between the two charges when the sphere is in equilibrium.

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Three equal point charges $q>0$ are at the vertices of an equilateral triangle of side $a$, in vacuum. Determine the charge $Q$ to be placed at the center of the triangle so that all four charges are in equilibrium.

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