9. An insulating solid sphere with radius a carries a nonuniform charge distribution, p(r) =ar (0 0 and r is measured radially outward from the center of the sphere. Concentric with this solid sphere is an insulating spherical shell with inner radius b and outer radius c, and carries a uniform charge distribution with total charge Q. Your answers may include: a, b, c, r,a, Q, or ε0. a. What are the SI units of a? b. Determine the total charge q on the solid sphere of radius a. c. Find the electric field (magnitude and direction) in the following regions: i. 0c

Constants and conversion qe = 1.60x10-¹⁹ C factors that may be useful: me=9.11x10-³¹ kg mp = 1.67x10-27 kg Surface area of a sphere = 4TR² Volume of a sphere = (4/3) лR³ Eo = 8.85x10-12 C²/N-m²

A point charge of 20 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 4 cm) which has a net charge of -90 nC. Determine the resulting charge density on the outer surface of the conducting sphere. A. -3483 nC/m? B. -5474 nC/m² C. 3483 nC/m? D. 5474 nC/m? E. -55732 nC/m?

A point charge of 40 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 4 cm) which has a net charge of -30 nC. Determine the resulting charge density on the outer surface of the conducting sphere. A. 497.6 nC/m² B. 3483 nC/m² C. 7962 nC/m² D. -497.6 nC/m2 E. -3483 nC/m²

1.Charge, Q= 2.20nC is uniformly distributed along the thin rodof length, L= 1.20m shown above. a.Determine the linear charge density of the rod. b.Determine an expression for charge dqon an infinitesimally small section of the rod of length dxin terms of the charge density and dx. c.The point P1is located a distance a= 0.300m from the end of the rod. Determine an expression for the distance, rbetween the point P1and an arbitrary chunk of the rod located an arbitrary distance xfrom the origin (between 0 and L). d.Determine an expression for the electric field dEat P1due to only the arbitrary chunk of the rod from part c. Use k, λ, x, L, and a. e.Determine the net electric field, Eat a point P1due to the entire rod.

The Oscilloscope 3. A solid insulating cylinder of radius A is surrounded by a hollow, concentric conducting cylinder of inner radius B and outer radius C. The solid cylinder has a non-uniform charge density given by p(r)= =+ +ßr where a and ß are constants. α r The conducting shell is uncharged. a. What is the total charge on the solid cylinder? b. What is the charge on the inner surface of the conducting cylinder? c. What is the charge on the outer surface of the conducting cylinder? d. What is the electric field everywhere (r C)?

The figure shows a solid non-conducting sphere of radius a = 4.4 cm. It is surrounded by a charged conducting spherical shell of inner radius b = 15.3 cm and outer radius c = 24.8 cm. The inner sphere has a net charge of q1 = 9 nC and the conducting spherical shell has a net charge of q2 = -7 nC.   a. What is the surface charge density on the inside surface of the spherical shell? b. What is the surface charge density on the outside surface of the spherical shell? c. What is the value of the electric field at a distance r = 58 cm from the centre of the spheres? Please use a negative value to indicate the electric field points toward the centre of the spheres and a positive value to indicate away from the centre of the spheres.

Constants and conversion qe = 1.60x10-¹⁹ C factors that may be useful: me=9.11x10-³¹ kg mp = 1.67x10-27 kg Surface area of a sphere = 4TR² Volume of a sphere = (4/3) лR³ Eo = 8.85x10-12 C²/N-m²

A 5 cm radius ball is charged to 190 nC. The charge is uniformly distributed throughout the volume of the ball. a. What is the charge density for this ball? ANS. 3.628733×10-4 C/m^3 b. How much charge is enclosed by a sphere of radius 1 cm concentric with the ball??

Three point charges are located in free space along the x-axis. A positive charge of +2 μC is located at x = 0, a negative charge of -3 μC is located at x = 3 m, and a positive charge of +4 μC is located at x = 6 m. a. Will q1 and q2 attract or repel? Blank 1 b. Will q1 and q3 attract or repel? Blank 2 c. What is the direction of the electrostatic force acting on q1 due to q2? (north, south, east, or west) Blank 3 d. What is the direction of the electrostatic force acting on q1 due to q3? (north, south, east or west) Blank 4 For the following questions, convert your answer into PROPER SCIENTIFIC NOTATION and round the coefficient to two decimal places.(e.g. 5.43 x 102; 5.43 is the coefficient) What is the magnitude of the electrostatic force on q1 due to q2? Blank 5 x10^Blank 6 N What is the magnitude of the electrostatic force on q1 due to q3? Blank 7x10^Blank 8 N Calculate the net electric force on the positive charge at x = 0 due to the other two charges: Blank 9 x 10^Blank 10 N