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 freeThe electron beam in a certain cathode ray tube possesses cylindrical symmetry, and the charge density is represented by \(\rho_{v}=-0.1 /\left(\rho^{2}+10^{-8}\right)\) \(\mathrm{pC} / \mathrm{m}^{3}\) for \(0<\rho<3 \times 10^{-4} \mathrm{~m}\), and \(\rho_{v}=0\) for \(\rho>3 \times 10^{-4} \mathrm{~m} .(a)\) Find the total charge per meter along the length of the beam; \((b)\) if the electron velocity is \(5 \times 10^{7} \mathrm{~m} / \mathrm{s}\), and with one ampere defined as \(1 \mathrm{C} / \mathrm{s}\), find the beam current.
A \(100-n C\) point charge is located at \(A(-1,1,3)\) in free space. \((a)\) Find the locus of all points \(P(x, y, z)\) at which \(E_{x}=500 \mathrm{~V} / \mathrm{m} \cdot(b)\) Find \(y_{1}\) if \(P\left(-2, y_{1}, 3\right)\) lies on that locus.
Given the surface charge density, \(\rho_{s}=2 \mu \mathrm{C} / \mathrm{m}^{2}\), existing in the region \(\rho<\) \(0.2 \mathrm{~m}, z=0\), find \(\mathbf{E}\) at \((a) P_{A}(\rho=0, z=0.5) ;(b) P_{B}(\rho=0, z=-0.5)\). Show that \((c)\) the field along the \(z\) axis reduces to that of an infinite sheet charge at small values of \(z ;(d)\) the \(z\) axis field reduces to that of a point charge at large values of \(z\).
A uniform line charge of \(16 \mathrm{nC} / \mathrm{m}\) is located along the line defined by \(y=\) \(-2, z=5\). If \(\epsilon=\epsilon_{0}:\) (a) find \(\mathbf{E}\) at \(P(1,2,3) .\) (b) find \(\mathbf{E}\) at that point in the \(z=0\) plane where the direction of \(\mathbf{E}\) is given by \((1 / 3) \mathbf{a}_{y}-(2 / 3) \mathbf{a}_{z} .\)
Find \(\mathbf{E}\) at the origin if the following charge distributions are present in free space: point charge, \(12 \mathrm{nC}\), at \(P(2,0,6) ;\) uniform line charge density, \(3 \mathrm{nC} / \mathrm{m}\), at \(x=-2, y=3 ;\) uniform surface charge density, \(0.2 \mathrm{nC} / \mathrm{m}^{2}\) at \(x=2\).
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