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Two long straight wires, carrying opposite uniform line charges
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- Consider a uniformly charged solid sphere of radius ? and total charge ? centered on the origin. In this problem you will calculate the potential ?(?) for ? < ? in two different ways. Use infinity as the reference point (i.e., ?(∞) = 0). (a) Use Eq. 2.21 of Griffiths to compute the potential at ? < ?. (b) Use Eq. 2.29 of Griffiths to compute the potential at ? < ?.arrow_forward(2.15) The electrostatic potential outside uncharged conducting cylinder in a uniform electric field is given by Ý = - Eor cos o + E̟ a² r¬1 cos o where Eo and a [E = - V] in cylindrical coordinates. are constants. Find E outside the cylinder Cartesian-Spherical Transformationsarrow_forwardVerify if the following vector fields are conservative: a) Ã = ( ) 2y 1+2²+y: 1+z²+y? b) Ã, = (2ry – 2², 2yz + x², y² – 2xz) In case they are conservative, find their respective potential fields.arrow_forward
- (a) What property of the Electric Field E allows us E can be expressed as a gradient of a scalar (V). (b) If you integrate Electric Field E along a path, say from point A to B, you get the potential difference between points B and A. If you integrate E along a closed loop what do you get?arrow_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) PLA=A nC/m 20° z=0 plane (0, 3, 0) p=3 PLB=1.5 nC/m 10° 10° p= 1.6 p=3.5 Psc=1 nC/m² 20° FIGURE 4.11 See Prob. 20.arrow_forwardCould the vector A = x 2 y i + x y 2j + e-βy sinαx k, where α and β are constant, be interpreted as a conservative electric field? If the answer is affirmative, find the potential V from which the electric field could be obtained. (The bold letters indicate vectors. Place the arrows on the vectors and the "hats" on the unit vectors.)arrow_forward
- Can someone please do this task step by step.Find the electric field (magnitude and direction) a distance z above the midpoint between twoequal charges q, a distance d apart (Fig. 6).arrow_forwardElectric potential is given as V=5.4sinecos/r2 (V/m) in a medium. Calculate the work done (in µJ) in moving a Q1=12.9 (µC) charge from point A(r= 1,0=30°,0=120°) to B(r=4,0=90°,0=60°) which are given in spherical coordinates. O a. 21.55 O b. 17.63 O . 19.59 O d. 23.51 О е. 15.67arrow_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. %3D (0, 5, 0)| PLA=A nC/m 20° z=0 plane (0, 3, 0) p= 3 PLB= 1.5 nC/m 10° 10° p=1.6 p= 3.5 Psc 1 nC/m2 20° FIGURE 4.11 See Prob. 20.arrow_forward
- 4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) P-I nC/m 20° z-0 plane (0, 3, 0) p-3 Pu=1.5 nC/m 10° p-1.6 10° p-3.5 PacI nCim? 20 FIGURE 4.1Iarrow_forwardThe space between the plates of a parallel-plate capacitor (Fig. 4.24) is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab-1 has dielectric constant of 2 and slab-2 has a dielectric constant of 1.5. With the area of each of the top and bottom conducting plates is much greater than a?, we can assume the the surface charge densities +o and -o on the top and bottom plates is uniform. (a) Find the electric displacement D in each slab. (b) Find the electric field E in each slab. (c) Find the potential difference between the plates. (d) Find the locations and amounts of all bound charge. (e) Based on the values of bound charge, recalculate E and verify your answer from (b). (f) How do your results relate to the formula for the addition of two series capacitors?arrow_forwardAn annulus has inner and outer radii a and b, respectively and carries a uniform surface charge density o (where sigma is a positive constant, the charge is distributed between the surface of disk of radius a and disk of radius b.) The annulus is on the xy plane as shown in the figure. A point positive charge of q and mass m is released at rest at z = 0 and slightly pushed (i.e., its initial speed is almost zero and can be ignored). Find the ultimate speed of the charge at z = o in terms of k (Coulomb's constant), o, a,b, m, and q. a. → Z q,m Select one: | 2tkqo(b - a m Tkqo(b – a) m 4r kqo(b – a) m 2nkqo(b – a) mab Tkqo (b – a) тabarrow_forward
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