Chapter 2: Problem 2
Point charges of \(1 \mathrm{nC}\) and \(-2 \mathrm{nC}\) are located at \((0,0,0)\) and \((1,1,1)\), respectively, in free space. Determine the vector force acting on each charge.
Chapter 2: Problem 2
Point charges of \(1 \mathrm{nC}\) and \(-2 \mathrm{nC}\) are located at \((0,0,0)\) and \((1,1,1)\), respectively, in free space. Determine the vector force acting on each charge.
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Get started for free(a) Find \(\mathbf{E}\) in the plane \(z=0\) that is produced by a uniform line
charge, \(\rho_{L}\), extending along the \(z\) axis over the range \(-L
A uniform volume charge density of \(0.2 \mu \mathrm{C} / \mathrm{m}^{3}\) is
present throughout the spherical shell extending from \(r=3 \mathrm{~cm}\) to
\(r=5 \mathrm{~cm}\). If \(\rho_{v}=0\) elsewhere, find \((a)\) the total charge
present throughout the shell, and \((b) r_{1}\) if half the total charge is
located in the region \(3 \mathrm{~cm}
An electric dipole (discussed in detail in Section 4.7) consists of two point charges of equal and opposite magnitude \(\pm Q\) spaced by distance \(d\). With the charges along the \(z\) axis at positions \(z=\pm d / 2\) (with the positive charge at the positive \(z\) location), the electric field in spherical coordinates is given by \(\mathbf{E}(r, \theta)=\left[Q d /\left(4 \pi \epsilon_{0} r^{3}\right)\right]\left[2 \cos \theta \mathbf{a}_{r}+\sin \theta \mathbf{a}_{\theta}\right]\), where \(r>>d\). Using rectangular coordinates, determine expressions for the vector force on a point charge of magnitude \(q(a)\) at \((0,0, z) ;(b)\) at \((0, y, 0)\).
Two identical uniform sheet charges with \(\rho_{s}=100 \mathrm{nC} / \mathrm{m}^{2}\) are located in free space at \(z=\pm 2.0 \mathrm{~cm}\). What force per unit area does each sheet exert on the other?
For fields that do not vary with \(z\) in cylindrical coordinates, the equations of the streamlines are obtained by solving the differential equation \(E_{p} / E_{\phi}=\) \(d \rho /(\rho d \phi)\). Find the equation of the line passing through the point \(\left(2,30^{\circ}, 0\right)\) for the field \(\mathbf{E}=\rho \cos 2 \phi \mathbf{a}_{\rho}-\rho \sin 2 \phi \mathbf{a}_{\phi}\).
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