A spherical ball that has radius R has a volume charge density p as shown below. Figure 2 Determine the electric field at the centre of the sphere if p is a function of x such that p(x) = ax, where a is a positive constant. {Hint: It is given that for a disk with uniform surface charge density o and radius r, the electric field in free space along |x| the central axis (x axis) is described by the expression E, (1 - 280 Vx2+r2
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- a) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.) Surface charge density σ2Give your answer up to at least three significance digits. b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.) Magnitude of the electric field at r=0.76mm Give your answer up to at least three significance digits. c) Calculate absolute value of the potential difference between the wire and the cylinder. Absolute value of the potential difference Give your answer up to at least three significance digits. d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm. Capacitance C for this cylindrical system Give your…What would be the electric field for z0 << R and z0 >> R for the following integral? The integral is the answer to the following question: "A uniformly charged disk with charge Q and radius R sits in the xy-plane with its center at theorigin. Take z0 to be some point on the positive z-axis. What is the electric field at z0? Leave your answer in the form of a well-defined definite integral."A positively charged cylinder has a uniform volume charge density. Height l is larger than its radius a (1»a). a P a. When Point P is very close to the surface of the cylinder (1>r>a), the electric field there can be derived by treating the cylinder as an = Eŝ. infinitely long one. Suppose that we already measure the electric field at P as charge density in terms of E and a (ŝ is the radial unit vector in the cylindrical coordinate system as defined in the Equation: now use the Gauss's law to find the volume cos o â + sin ø ŷ, - sin ø Âx + cos ø ŷ, î. b. Now we move the detector from Point P to Point Q, which is so far away from the cylinder (R>l>a), that the cylinder can be treated as a point. Based on result in Part (a), find out the electric field at Q (Note that OQ is in the x direction.)
- A quarter-disc in the first quadrant has a surface charge density given by Kcos(φ)C/m2 . If the radius of the disc is b, calculate the electric field at a point P(0, 0, −h).Consider any charge distribution with a charge density e(7), let v be a spherical region of radius Y.. Centered at 0, the average electric field E within v has the formula: 1 E: Iar / E(F)dv = Ent + Eot %3D where Ent is the average field due to all internal charges v and Eetis the average field due to all external charges v Prove that Eint 1 4T€0 r3 Eext p(T) du' Jv 4T€0 p13 where p is the electric dipole moment (cycle O) of the internal charge. and V is the region in space. that includes v and P(F)# 0 3= Three uniform charge distributions are present in a region: an infinite sheet of charge, a finite line charge, and a ring of charge. The infinite sheet of charge at (x, -3, z), where x and z spans from negative to positive infinity, has a charge density Ps 5 nC/m². The finite line charge at (0, -1, z), where z ranges from -2 to 2, has a charge density -4 nC/m. Finally, the ring of charge, with a radius of 3m and charge density PL 2 nC/m, is parallel to the xz-plane centered at (0, 4, 0). All coordinates are in meters. Use the value k = 9 x 10⁹ in your solutions and = answers. Question: Determine the magnitude the electric field due to the infinite sheet charge only at (0, 2, 0).
- A spherical cloud has a uniform negative charge density -Pv and is located above ground, as shown in Figure below. The dimensions and charge density are shown in the same figure: (a) Calculate the electric field intensity everywhere at ground level. (b) What is the largest electric field intensity at ground level? Where does it occur? (c) Calculate the charge density on the ground. cloud a -Pv km d= 2 km Į Ground (conductor)An infinitely long cylinder in free space is concentric with the z-axis and has radius a. The net charge density p in this cylinder is given in cylindrical coordinates by, 1 a² +r² where A is a constant. (a) Show that the total charge per unit length, λ in the cylinder is λ = πA ln 2. p(r) = A- Hint: you may find the following integral useful. 1 2 J for r a) and inside the cylinder (r< a). (d) The cylinder is composed of a material in which the polarisation P is given by P = P₁² in (1 +5²) e₁₁ er, r where Po is a constant. Determine the bound charge density pb in the cylinder. Hence, or otherwise, determine a relation between A and Po such that the free charge density of in the cylinder vanishes.Charge density p Figure 2: (True,False) (a) The electric field inside the sphere is given by Ē = (7 – b) An insulating sphere of radius R has a spherical hole of radius a located within its volume and centered a distance b from the center of the sphere where a < b < R(a cross section of the sphere is shown in figure 2). The solid part of the sphere has a uniform volume charge density p: (b) The electric field inside the hole is constant and is given by : (F – 6) = (True, False) -デ+ E = Ësphere + E(-p) 3e0 3e0 3€0 - 2rb cos 0: (c) The electric field inside the sphere of radius R but outside the hole of radius a is not constant and is given by |7–6| = /r2 + b² -pa3 デー5 デ+ (True, False) - 6|3 E = Ësphere + Ē(-P) 3e0 3e0 F –An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aRT E(r) : 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.You have been given the following charge density function for r ≤ R elsewhere P Po (1-r/R) 0 This charge density function describes a long cylindrical charge distribution. Please explain your steps and determine the electric field everywhere due to this charge distribution.SEE MORE QUESTIONS