Problem 1: UP 6.46 A total charge Q is distributed uniformly throughout a spherical shell of inner and outer radii ₁ and 12, respectively. Show that the electric field due to the charge is r≤r₁ 1₁ ≤r ≤r₂ 0, Q E(r)=4neor²r²³ - r³, 1 Q 4περ 12 Î, f, r≥ 12
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- A solid conducting sphere, which has a charge Q1 =84Q and radius rg = 1.5R is placed inside a very thin spherical shell of radius rp = 3.4R and charge Q2 =15Q as shown in the figure below. Q2 Tb Q1 ra Find the magnitude of the electric field at r=6.2. Express your answer using one decimal point in units 1 where k = 4περ of kProblems 11-13 refer to the following situation. A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: Problem 11: What is the constant po? Q πR³ a. Po and R are positive constants. The total charge of the distribution is Q. Problem 12: What is the E-field for r R? 1 Q b. 4περ 12 a. p(r) = {Po (7) . 20 πR³ 1 Qr² 4περ R4 1 QR 4περ 13 C. C. r R C. 30 πR³ 1 Qr³ 4περ R5 QR² 1 4περ 14 d. d. d. 4Q πR³ 1 Qr4 4πεο R6 QR³ 1 Απο 15A solid conducting sphere, which has a charge Q, =28Q and radius ra = 2.2R is placed inside a very thin spherical shell of radius rp = 6.7R and charge Q2 =14Q as shown in the figure below. Q2 ra Find the magnitude of the electric field at r=3.3. Express your answer using one decimal point in units of k where k = 4περ
- Charge Q is uniformly distributed in a sphere of radius R. (a) What fraction of the charge is contained within the radius r = R/2.00? (b) What is the ratio of the electric field magnitude at r =R/2.00 to that on the surface of the sphere?A solid conducting sphere, which has a charge Q1=38Q and radius ra= 1.3R is placed inside a very thin spherical shell of radius rp = 7.6R and charge Q2 =-10Q as shown in the figure below. Q1 ra Find the magnitude of the electric field at r=4.7. Express your answer using one decimal point in units 1 where k = of k 4πεοA positively charged particle is held at the center of a spherical shell. The figure gives the magnitude E of the electric field versus radial distance r. The scale of the vertical axis is set by Es = 11.0 × 107 N/C. Approximately, what is the net charge on the shell? Assume rs = 1 cm. Number i E (107 N/C) E 0 Units r's 2rs r (cm) I 3rs 4rs 5rs
- Electric charge is distributed over the disk a2 + y < 20 so that the charge density at (x,y) is o(x, y) = 5 + x² + y² coulombs per square meter. Find the total charge on the disk.A thick insulating cylindircal shell of inner radius a=2.5R and outer radius b=5.2R has a uniform charge density p . What is the magnitude of the electric field at r=8.2 R ? Express your answer using one decimal place in units of ?The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs1.0 m; p(r)= 5p,(1-r/3) For r> 1.0 m; p(r)= 0, where r is in meters. What is the value of r in meters for which the electric field is maximum? O 0.25 O 0.50 О 0.75 O 1.00 O 2.00 О 3.00
- Figure (a) shows a nonconducting rod with a uniformly distributed charge +Q. The rod forms a 10/25 of circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P (see Figure (b)), by what factor is the magnitude of the electric field at P multiplied? (a) +Q Number R i P MI Units +Q |—R— P This ansA thick insulating cylindircal shell of inner radius a-1.5R and outer radius b=5.1R has a uniform charge density p. What is the magnitude of the electric field at r=9.4 R ? Express your answer using one decimal place in units of PR :?What total (excess) charge q must the disk in Fig. have for the electric field on the surface of the disk at its center to have magnitude 3.0 ×108 N/C, the E value at which air breaks down electrically, producing sparks? Take the disk radius as 2.5 cm. (b) Suppose each surface atom has an effective cross-sectional area of 0.015 nm2. How many atoms are needed to make up the disk surface? (c) The charge calculated in (a) results from some of the surface atoms having one excess electron. What fraction of these atoms must be so charged?