Electric field

Compute the magnitude of the electric field produced by a point charge $Q=6.0\mathrm{nC}$ at distance $r=20\mathrm{cm}$, and determine its orientation.

Solution available to those who have unlocked the subject.

At what distance from a point charge $Q=2.0\mathrm{nC}$ does the electric field have magnitude $500N/C$?

Solution available to those who have unlocked the subject.

An electron is in a uniform electric field of magnitude $E=3.0\cdot 10^{3}N/C$. Compute the magnitude of the force it experiences and of its acceleration, and indicate the orientation of the force with respect to the field.

Solution available to those who have unlocked the subject.

The charges $q_1=1.0\mathrm{nC}$ and $q_2=9.0\mathrm{nC}$ are at rest on the $x$-axis, at $x=0$ and at $x=40\mathrm{cm}$. Find the point of the $x$-axis at which the electric field is zero.

Solution available to those who have unlocked the subject.

Two charges $q=2.0\mathrm{nC}$ are at rest at $(0,0)$ and at $(6.0\mathrm{cm},0)$. Compute the electric field at the point $P=(3.0\mathrm{cm},4.0\mathrm{cm})$.

Solution available to those who have unlocked the subject.

Two charges $q=3.0\mathrm{nC}$ occupy two vertices of an equilateral triangle of side $a=10\mathrm{cm}$. Compute the magnitude of the electric field at the third vertex and indicate its direction.

Solution available to those who have unlocked the subject.

A dipole is formed by the charges $\pm 1.5\mathrm{nC}$ at distance $d=1.0\mathrm{mm}$. Compute the dipole moment and the electric field on the axis of the dipole at $r=5.0\mathrm{cm}$ from the center.

Solution available to those who have unlocked the subject.

A dipole with $p=3.0\cdot 10^{-12}\mathrm{C}\cdot \mathrm{m}$ is in a uniform field $E=4.0\cdot 10^{4}N/C$. Compute the maximum torque of the electric forces on the dipole and the work that an external agent must do to rotate it slowly from the position of stable equilibrium to that of unstable equilibrium.

Solution available to those who have unlocked the subject.

A thin ring of radius $R=4.0\mathrm{cm}$ has charge $Q=8.0\mathrm{nC}$ uniformly distributed. Compute the electric field on the axis at distance $z=3.0\mathrm{cm}$ from the center.

Solution available to those who have unlocked the subject.

A very long straight wire, uniformly charged, produces at a distance of $10\mathrm{cm}$ a field of magnitude $900N/C$ directed toward the wire. Compute the linear charge density.

Solution available to those who have unlocked the subject.

A thin disk of radius $R=3.0\mathrm{cm}$ has uniform surface density $\sigma =2.0\cdot 10^{-6}C/{\mathrm{m}}^2$. Compute the electric field on the axis at distance $z=4.0\mathrm{cm}$ from the center.

Solution available to those who have unlocked the subject.

Two parallel infinite planes have uniform charge densities $+3.0nC/{\mathrm{m}}^2$ and $-3.0nC/{\mathrm{m}}^2$. Compute the electric field between the planes and outside.

Solution available to those who have unlocked the subject.

A proton, of mass $m_p=1.67\cdot 10^{-27}\mathrm{kg}$, enters with velocity $v_0=2.0\cdot 10^{5}m/s$ perpendicular to the field a region of length $\ell =4.0\mathrm{cm}$ where there is a uniform field $E=1.0\cdot 10^{3}N/C$. Compute the lateral displacement of the proton at the exit from the region.

Solution available to those who have unlocked the subject.