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 free(a) Find the electric field on the \(z\) axis produced by an annular ring of uniform surface charge density \(\rho_{s}\) in free space. The ring occupies the region \(z=0, a \leq \rho \leq b, 0 \leq \phi \leq 2 \pi\) in cylindrical coordinates. \((b)\) From your part (a) result, obtain the field of an infinite uniform sheet charge by taking appropriate limits.
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 \(100-n C\) 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.
(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
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 \((0, y, 0)\).
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