The clectric potential in a region of space is V (x, y) 200 Volts, where x and x²+y² y are in meters. What are the strength and direction of the clectric ficld at (x, y) = (2.0 m, 2.0 m)? Give the direction as an angle cw or ccw (specify which) from the positive r-axis.
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- Find the capacitance (in F) of a parallel plate capacitor having plates of area 6.00 m2 that are separated by 0.300 mm of Teflon.A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 cm , and the outer sphere has radius 16.5 cm . A potential difference of 140 V is applied to the capacitor. What is the energy density at r= 10.1 cm , just outside the inner sphere? What is the energy density at r = 16.4 cm , just inside the outer sphere?Consider the capacitor network. 21.9 µF T44.2 V 1.77 pF 1.4 µF 8.78 µF What is the equivalent capacitance of the network? Answer in units of uF. t Find the charge on the 1.77 µF capacitor to the far left.
- Consider the potential differences between pairs of points as shown. What are the magnitudes of the potential differences ΔV14, ΔV24, and ΔV34?What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 3.2 mm of teflon with a dieletric constant of 2.1?Derive an expression for the capacitance of two concentric hollow spherical conductors of radii r and R. What value do you get for the capacitance when r=4.5 m and R=29.25 m?
- Find the capacitance (in µF) of a parallel plate capacitor having plates of area 8.00 m2 that are separated by 0.300 mm of Teflon.A thin-walled, hollow, conducting cylinder with radius rb is concentric with a solid conducting cylinder with radius ra<rb. Each has length L. The two cylinders are attached by conducting wires to the terminals of a battery that supplies potential V. A solid cylindrical shell, with inner radius ra and outer radius R<rb, made of a material with dielectric constant K, slides between the conducting cylinders, as shown in (Figure 1). By changing the insertion distance x, we can alter the capacitance seen by the battery and therefore alter the amount of charge stored in this device. a)Determine the capacitance as a function of x. Express your answer in terms of the variables K, L, ra, rb, R, x, and constants ϵ0, π. b) If L = 12.0 cm, ra = 1.00 cm, rb = 4.00 cm, R = 3.00 cm, and K = 3.21, what is the capacitance when x = 0? c) What is the capacitance when x = L? d) What value of x results in 6.00 nC of charge on the positively charged cylinder plate when V = 1.00 kV?In a linear particle accelerator electrons are accelerated from rest to a speed of approximately the speed of light (3 x 108 m/s). If point A is the initial position of the electrons in the machine and point B is the position at which they reach their final speed, what is the electrical potential difference VA - VB in MV?
- The diagram below depicts a cross section of coaxial conductor with an inner wire of diameter di and an outer conducting sheath of inside diameter do, and some material placed in the space between the two wires. Suppose that you have a coaxial wire with di=1.3 mm and do=7.55 mm, and we put mylar (κ=3.1) in the space between the two wires. If there is a potential of 1 kV between the wires, how much energy is stored in a 10 m piece of cable? For my answer I got 5.32 J which was wrong.Consider two long, parallel, and oppositely charged wires with linear charge density +λ and -λ of radius r with their centers separated by a distance D (? ≫ ?). Show that the capacitance per unit length of this pair of wires is given by the following, and show the work required to set up an integral for E, ∆? and then finding C.In this figure, C1= 9.1 μF, C2= 4.2 μF, C3= 5.2 μF. The equivalent capacitance of the combination is C1 C2 HHH C3 μF. Express your answer in normal format (NOT exponential format) with 3 SF.