Two equal charges of the same sign are separated by a distance of 2
d. Calculate the electric field
vector at the points along the perpendicular bisector of the line joining the two charges. Check the
solution for points far away from the center of the dipole.
Two equal charges of the same sign are separated by a distance of 2
d. Calculate the electric field
vector at the points along the perpendicular bisector of the line joining the two charges. Check the
solution for points far from the charges.
Two identical charges of the same sign are separated by a distance of 2
d. The magnitude of the
electric field at the points along the perpendicular bisector of the line joining the two charges is
given by
\[
\begin{gather}
E=\frac{1}{4\pi \epsilon_0}\frac{2qy}{\left(a^2+y^2\right)^{3/2}}
\end{gather}
\]
Determine:
a) The points along the
y-axis, for which the magnitude of the electric field assumes its maximum
value;
b) The magnitude of the maximum electric field.
Electric Field of a Continuous Charge Distribution
A ring of radius a carries a uniformly distributed electric charge Q. Calculate the
electric field vector at a point P on the symmetry axis perpendicular to the plane of the ring
at a distance z from its center.
A ring of radius
a is uniformly charged with a charge
Q. The electric field produced by this
ring at points on the axis of symmetry perpendicular to the plane of the ring at a distance
z is
given, in magnitude, by
\[
\begin{gather}
E=\frac{1}{4\pi \epsilon_{0}}\frac{Qz}{\left(a^{2}+z^{2}\right)^{3/2}}
\end{gather}
\]
Determine:
a) For what values of z is the electric field maximum?
b) What is this maximum value.
Two concentric rings are located on the same plane. The ring of radius
R1 has a charge
Q1, and the ring of radius
R2 has a charge
Q2. The
electric field vector produced by a ring of radius
r at a distance
z from the center is
given by
\[
\begin{gather}
\mathbf{E}=\frac{1}{4\pi \epsilon_0}\frac{Qz}{\left(r^2+z^2\right)^{3/2}}\;\mathbf{k}
\end{gather}
\]
Determine the electric field vector:
a) In the common center of the two rings;
b) At a point located at a distance z, much greater than
R1 and
R2.
An arc of a circle of radius a and central angle θ0 carries an electric charge
Q uniformly distributed along the arc. Determine:
a) The electric field vector, at the points of the line passing through the center of the arc and is
perpendicular to the plane containing the arc;
b) The electric field vector in the center of curvature of the arc;
c) The electric field vector when the central angle tends to zero.
A ring of radius a carries a uniformly distributed electric charge q1 in one of
the halves and q2 in another half. Calculate the electric field vector at a point
P on the symmetry axis perpendicular to the plane of the ring at a distance z from its
center.