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 freeWithin 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, \(r \leq a\) \(0 \leq \theta \leq 0.1 \pi, 0 \leq \phi \leq 0.2 \pi\)
Two point charges of equal magnitude \(q\) are positioned at \(z=\pm d / 2 .(a)\) Find the electric field everywhere on the \(z\) axis; \((b)\) find the electric field everywhere on the \(x\) axis; \((c)\) repeat parts \((a)\) and \((b)\) if the charge at \(z=-d / 2\) is \(-q\) instead of \(+q\).
A uniform line charge of \(2 \mu \mathrm{C} / \mathrm{m}\) is located on the \(z\) axis. Find \(\mathbf{E}\) in rectangular coordinates at \(P(1,2,3)\) if the charge exists from \((a)-\infty<\) \(z<\infty ;(b)-4 \leq z \leq 4\).
A 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?
Let a point charge \(Q_{1}=25 \mathrm{nC}\) be located at \(P_{1}(4,-2,7)\) and a charge \(Q_{2}=60 \mathrm{nC}\) be at \(P_{2}(-3,4,-2) .(a)\) If \(\epsilon=\epsilon_{0}\), find \(\mathbf{E}\) at \(P_{3}(1,2,3) .\) (b) At what point on the \(y\) axis is \(E_{x}=0\) ?
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