Find the electric field vector on the x-axis at x xo due to an infinite line cha

Question

Find the electric field vector on the x-axis at x xo due to an infinite line charge extending on the y-axis from zero to minus infinity. Assume the surrounding medium is vacuum and the line charge hasa uniform density 7. A series RLC circuit is driven by a generator with a magnitude of 30 volts and a frequency of 1000 rad/s. Find the voltage as a function of time across the 1-uF capacitor (phase measured relative to the generator) if the resistor is 300 ohms and the inductor is 600 mH. 8. An infinite series of nested, concentric, thin spherical shells have radius 2r, 4r, 6r, 8r, and so on, and each carries a uniform surface charge distribution , Find the electric field magnitude 9r from the common center. The interspersed medium has permittivity 9·The switch in the circuit in the nearest diagram has been in the position shown for a very long time. Find an expression, simplified as far as reasonably possible, for the charge magnitude in the capacitor at time t after the switch moves according to the arrow 10. Find the electric potential at (-3-2.7) with respect to (-4,0,5) in an electric field given by E-4x-23y in newtons per coulomb

Explanation / Answer

At x= xo
consider an element of the infinitely long wire of length dy
Electric field due to this elemenrt = dE
dE = k*dq(xo i + y j)/(xo^2 + y^2)^3/2 = k*(lambda)dy(xo i + y j)/(xo^2 + y^2)^3/2
let y = xotan(theta)
dy = xo*sec^2(theta)d(theta)
dE = k*lambda*(xo i + xo*tan(theta) j)*xocos(theta)d(theta) / xo^3 = k*lambda*(cos(theta)d(theta) i + sin(theta)d(theta) j)/xo
Integrating from theta = 0 to theta = -90 deg
E = k*lambda*( + j)/xo + k*lambda*( i )/xo = k*lambda[ i + j]/xo

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