Chapter 2: Problem 10
A charge of \(-1 \mathrm{nC}\) is located at the origin in free space. What charge must be located at \((2,0,0)\) to cause \(E_{x}\) to be zero at \((3,1,1)\) ?
Chapter 2: Problem 10
A charge of \(-1 \mathrm{nC}\) is located at the origin in free space. What charge must be located at \((2,0,0)\) to cause \(E_{x}\) to be zero at \((3,1,1)\) ?
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Get started for freeA spherical volume having a \(2-\mu \mathrm{m}\) radius contains a uniform volume charge density of \(10^{15} \mathrm{C} / \mathrm{m}^{3}\). (a) What total charge is enclosed in the spherical volume? (b) Now assume that a large region contains one of these little spheres at every corner of a cubical grid \(3 \mathrm{~mm}\) on a side and that there is no charge between the spheres. What is the average volume charge density throughout this large region?
Within a region of free space, charge density is given as \(\rho_{v}=\frac{\rho_{v} r \cos \theta}{a} \mathrm{C} / \mathrm{m}^{3}\), where \(\rho_{0}\) and \(a\) are constants. Find the total charge lying within \((a)\) the sphere, \(r \leq a ;(b)\) the cone, \(r \leq a, 0 \leq \theta \leq 0.1 \pi ;(c)\) the region, \(r \leq a\) \(0 \leq \theta \leq 0.1 \pi, 0 \leq \phi \leq 0.2 \pi\)
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.
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 \(x=2\).
If \(\mathbf{E}=20 e^{-5 y}\left(\cos 5 x \mathbf{a}_{x}-\sin 5 x \mathbf{a}_{y}\right)\), find \((a)|\mathbf{E}|\) at \(P(\pi / 6,0.1,2) ;(b)\) a unit vector in the direction of \(\mathbf{E}\) at \(P ;(c)\) the equation of the direction line passing through \(P\).
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