(a) What is the magnitude of the electric field in a region where the potential is given by the expression V = ax2 + b where a = −600 V/m2 and b = 195 V? (Substitute numerical values, and express your answer in terms of x. Assume SI units, but do not include units in your answer.) E =  V/m2   (b) What is the magnitude of the electric field at x = 6.25 m?  V/m

Given cylindrical capacitor of length = 61.4044 m where the radius of the inner plate is R₁ = 6.2696 m and the outer plate is R2 = 40.7022 m. The capacitor is charged with charge Q = 3 × 10-4 C Three cylindrical conductors of width d= 0.56 m are inserted into the capacitor: Two cylindrical conductors inserted concentrically in between the capacitor plates and the third conductor is inserted concentrically inside the first plate, as seen in the figure below: Top view (a) R₂ Given that a = 3.2696 m b = 11.2696 m c = 14.2696 m How much energy (in Joule) is lost in the process? Top view (b)

Problem 2: Consider the parallel-plate capacitor shown in the figure. The plate separation is 5.9 mm and the the electric field inside is 24 N/C. An electron is positioned halfway between the plates and is given some initial velocity, v₁. Randomized Variables d = 5.9 mm E = 24 N/C + + + + + + + + d Otheexpertta.com Part (a) What speed, in meters per second, must the electron have in order to make it to the negatively charged plate? Part (b) If the electron has half the speed needed to reach the negative plate, it will turn around and go towards the positive plate. What will its speed be, in meters per second, when it reaches the positive plate in this case? select part Vf,b=1

A From Equation 25.6, we have the following. AV = -Ed = -(7.2 × 104 v/m)(0.60 m) = B V From Equation 25.3, we have the following. AU = qAV = eAV = (1.6 x 10-19 C)(AV) | The negative sign means that the potential energy of the system decreases as the proton moves in the direction of the electric field. This decrease is consistent with the conservation of energy in an isolated system: as the proton accelerates in the direction of the field, it gains kinetic energy and at the same time the system loses electric potential energy. The increase in kinetic energy of a charged particle in an electric field is exploited in many devices, including electron guns for TV picture tubes and particle accelerators for research in particle physics. You can predict and observe the speed of the proton as it arrives at the negative plate for random values of the electric field using this Interactive Example. Hints: Getting Started | I'm Stuck Exercise 25.2 For the previous example, apply the principle of…

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For problem 4 part b in square centimeters using inner and outer radii of the spherical capacitor of a = 5.49 cm and b = 1.05 a, respectively. (Answer In 5 sig. figs.)

An electric potential produced by some distribution of charge in a region is given by the equation V= 4xy2 - 3z²x + 15y²z with V in volts and the coordinates in meters. Determine the z-component of electric field (in kV/m) at the point (1.0, 3.0, 2.0) m.

Part (a)  Write an equation for the change of electric potential energy ΔU of the proton, in terms of the symbols given and the charge of the proton e.  ΔU = ______ Part (b)  Solve for the numerical value of the change of the electric potential energy in electron volts (eV).  ΔU = ______ Part (c)  How much work is done by the electric force during the motion of the proton in J?  W = _______

Consider a parallel-plate capacitor constructed of two square plates, 4.22 m on a side, separated by a distance 6.23 mm. If a charge of 2.85 nC is placed on one plate, with an equal but opposite charge on the other plate, find the electric field inside the capacitor. Answer in units of V/m.

A parallel plate capacitor has the space between its plates filled with 1.4 mm of paper and 3.9 mm of teflon, as shown in the figure on the right. If the area of the plate of a capacitor is 9.2 cm², what is the capacitance of the capacitor? (Express your answer in pF (i.e. picofarads) Answer: