Given a non-uniform SURFACE charge density o= 00 sin 0 cos? p, oo = constant, 0, pie spherical coordinate angles: 11. Find the total "Q" placed on a sphere of radius "R" centered on the origin
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- Consider a spherical shell with radius R and surface charge density a= ao cos 0, where is the polar angle in spherical coordinates and the shell is centered at the origin. a) Without computing any integral, argue why is the total charge carried by the shell zero. b) Evaluate the charge carried by the upper hemisphere, in terms of 0.Please AsapA solid insulating sphere of radius R =5.00 cm has a non-uniform charge density p = Por2, where r is measured from the center of the sphere and po is constant. Concentric with this sphere is a conducting spherical shell with inner radius a = 7.00 cm and outer radius b = 9.00 cm, having a net charge q = -1.00 µC. a) Find the value for the constant po (including units), given that the total charge on the insulating sphere is Q = 4.00 nC. Be sure to first derive expression in symbolic form in terms of Q, R. Box both the symbolic expression and the final answer. b) Derive an expression for electric field forr b. Box it. e) Draw an E vs. r graph and show the values for E at distances R, a, b.
- A uniformly charged conducting sphere of 1.7 m diameter has a surface charge density of 8.7 µC/m². (a) Find the net charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? (a) Number (b) Number i Units UnitsA total amount of positive charge Q is spread onto a thin non-conducting circular annulus of inner radius a and outer radius b. The charge is distributed in a way so that the charge density per unit area is given by ? =??3, where r is the distance from the center of the annulus to any point on it and k is a constant.(a) Find an expression for the total charge Q on the annulus. (b) Find an expression for the potential V at the center of the annulus in term of Q, a and b+8.0 µC and Qc = -2.0 µC. Consider three charges, QA = +6.0 µC, QB Charge Qais placed at point A = (-4.0,0) cm, charge QB is placed distance 4.0 cm from the origin, so that the line connecting it with origin makes an angle 0 = 60° with the negative x axis and charge Qc is at the origin. y QB QA What is the magnitude and direction of the electric force exerted by charges QA and QB on charge Qc?
- Given a non-uniform SURFACE charge density o= ko r z cos q, ko constant, r, o,z are cylindrical coordinate variables 12. Find the total "Q" placed on a closed cylinder of radius "R" and length "L" centered on the origin with one base in the x-y plane, along the positive z-axis.Given a constant SURFACE charge density o=00 : 3. Find the total "Q" placed on a disk of radius "R" 4. Find the total "Q" placed on a sphere of radius "R" 5. Find the total "Q" placed on a open cylinder of radius "R" and length "L" 6. Find the total "Q" placed on a closed cylinder of radius "R" and length "L"Auniformly charged conducting sphere of 1.7 m diameter has a surface charge density of 9.5 µC/m². (a) Find the net charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? (a) Number i 9.08 Units (b) Number 9.75e+6 Units
- An arch of radius r = R has the charge of Q between ≤ ≤of nonuniform linear charge Ꮎ density given by λ = sin(0). Which of the followings is the constant ? a) b) d) R 6Q (2-√2)R √2R 8Q (√2-1)Rneed helpA hollow sphere of radui R has a uniform nagative surface charge density -\sigma on its surface and a positive point charge +Q at its center. The charge Q is greater than the absolute magnitude of the total charge on the surface. The direction of the E-field is radially outward both inside and outside the sphere. What is the magnitude of the E-field inside the sphere at a distance r<R from the center? What is the magnitude of the E-field outside the sphere at a distance r<R from the center?