2.1 2.2 2.3 2 BALL AND PLANE Consider a spherical shell of radius R and charge...
2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area σ1 sitting at the origin. There is also an infinie plane parallel to the x- y plane sitting at z-zo with charge per unit area Oz. We will take Zo > R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo,0,0) with xo> R 2.3 15 POINTS The point (X1, 0,21) with 0 <...
16a: An "are" of radius R and linear charge density λ-Xo sin φ lies in the xy plane. It extends an angle of o above and below the x-axis. Determine the electric field at the origin. b: Determine the z-component of the electric field at the point (0,0, zo) but this time assume that λ--X- IR
2.1 2.2
2 FUNDAMENTAL THEOREMS Consider the vector function u x2+ yj)+12. 2.1 15 POINTS Verify the divergence theorem for a hemisphere of radius R centred at the origin, namely x2+y+22s R2 and z20. 2.2 15 POINTS Verify the Curl theorem (Stokes' theorem) for a circle of radius R in thex-y plane centred at
2. A thin ring of radius R in the x - y plane is centered at the coordinate origin, and is charged with linear charge density λ which depends* on the polar angle θ as (9) λο sin(0), where 0 > 0, and θ . (a) Plot λ(0) for θ [0.2n]. (b) Before doing any calculations, sketch the electric field vector vector at the coor- - 0 is on the positive r-axis dinate origin in the direction you expect it...
The 5th page of lecture 24:
2. Consider a circular current loop of radius R placed in the xy plane as shown in the figure. It is centered at the origin and viewed down from the positive z-axis the current, lo, flows anti-clockwise. Radius = R a. In what direction does the magnetic field point at the red point in the figure, Fa? Explain clearly why this is true. current b. Since B-VxA, in which plane does Alie. Explain clearly...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
Q8 (15 points): A spherical shell of radius R-10 cm, mass M-2 kg rolls smoothly ona horizontal surface due to a force P--15i N. The force is applied to a point on the shell that is 1.4R high from the ground. The acceleration of the center of mass is а--6Зі m/s2. i. What is the force of friction in unit vector notation? ii. What is the angular acceleration of rolling? ii. How much work is done by the force P...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...