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- Determine the volume charge density, in pC/m3, at (3, -8, -2) if the electric field present in the region is E = sin (3 x + 2 y + 3 z) V/m. All coordinates are measured in meters.Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/ao + B/r + bo %| where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Va Edr= Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-"b/ao - era/ao) + B In( ) + bo ( ))9:09 P A 98 You 9 minutes ago 2. Determine the electric field a distance z above the center of a large square loop of side a, if it carries a uniform charge A. You may use the result for the electric field at a distance z ahove a midpoint of a straight wire with constant A. After Griffiths, problem 2.4.
- Ex : A particle ( mass = 5.0g, charge = 40mC ) move in a region of space where the electric field is uniform and is given by E, = 2.5N/c,Ey = E, = 0. If the velocity of particle at t 0 is given by vy = %3! 50m/s,v = v,y = 0, what is the speed of particle at t= 2. Os.electrons radius r Two protons (p) and two (e) are arranged on a circle of 5 [cm], with angles 0₁ = 20°, 0₂ = 60°, 03 = 20° and 04 = 60°, as shown in the figure. (qp = +1.6 x 10-19 [C] and qe = -1.6 × 10-19 [C]). The figure is not to scale. 04 y a. Find Enet, the net electric field vector produced at the center of the circle. Enet = ([ ])i + ( ]) Ĵ [N/C] b. Where on the circle should a fifth point charge qo be placed (give its angle relative the +x-axis) and what is its value (calculate qo) in order to have Ēnet (the net electric field at the center of the circle) equals zero (Type the detailed solution to this question in the below box, Show all your calculation steps by typing in the box). P X20 sin 0 If V : - V in free space, find: (a) py at P(r = 2,0 = 30°, Ø = 0);
- If a proton and electron are released when they are 2.0 m apart, find the initial acceleration of electron (in m/s2) The answer (in fundamental SI unit) is... Path of trajectory AV w An electron is fired at a speed v¡ = 3.4 x 106 m/s and at an angle 0; = 30.5° between two parallel conducting plates as shown in the figure. If s = 1.5 mm and the voltage difference between the plates is AV = 98 V, determine how close, w, the electron will get to the %3D %3D bottom plate. Put your answer in meters and include at 6 decimal places in your answer. Do not include units. The x-axis of the coordinate system is in the middle of the parallel plate capacitor. Round your answer to 6 decimal places.Ex. 4: A metal sphere of radius 1 cm is charged with 3.14 u C. Find the electric intensity at a distance 1 m from centre of metal sphere.
- Calculate the magnitude of the electric field at a point which is 10 cm from a positive 23 μC charge. Use 1 Απερ = 9 × 10⁹ m/F. Answer: V/m3. You are designing an electron accelerator to bring a stationary electron to a speed of (1.210x10^7) m/s in a uniform electric field. If the acceleration time is (7.85x10^0) µs, what must the magnitude of the electric field be in N/C?Answers: a) 3.3 C c/m² 6. Two electrons are fixed 2.00 cm apart. Another electron is shot from infinity and comes to rest midway between the two. What was its initial speed? Answer: 318 m/s