BWC21103 ELECTROMAGNETISM

Tutorial 4

1. Let us illustrate the use the vector form of Coulomb’s law by locating a charge of Q1 = 3 x 10-4 (C) at (1, 2, 3) at a charge Q2 = -10-4 (C) at (2, 0, 5) in a vacuum. We desire the force exerted on Q2 by Q1. (Ans: F12=−10 ax+20a y−20az).

Solution

2. Point charges 1 mC and -2mC are located at (3, 2, -1) and (-1, -1, 4), respectively. Calculate the electric force on a 10 nC charge located at (0, 3, 1) and the electric field intensity at that point. (Ans: E=−650.7ax−381.7 a y+750,6 azkV/m)

Solution

3. A circular ring of radius a carrier a uniform charge ρL C/m and is placed on the xy-plane with axis the same as the z-axis.(a) Show that

E (0 , 0 , h )=ρL αh

2 ε0 [h2+α 2 ]3 /2 az

(b) What values of h gives the maximum value of E? (Ans: h=± α√2

)

(c) If the total charge on the ring is Q, find E as α→ 0. (Ans:E= Q4 π ε0 r2 az)

Solution

4. The finite sheet 0 < x < 1, 0 < y < 1 on the z =0 plane has a charge density

ρ s=xy ( x2+ y2+25 )32 nC/m2. Find

(a) The total charge on the sheet. (Ans: Q = 33.15 nC)(b) The electric field at (0, 0, 5). (Ans: (-1.5, -1.5, 11.25) V/m)(c) The force experienced by a – 1 mC charge located at (0, 0, 5) (Ans: (-1.5, -1.5, 11.25)

mN)

Solution

5. Determine D at (4, 0, 3) if there is a point charge -5π mC at (4, 0, 0) and a line charge 3π mC along the y axis. (Ans: D = DQ + DL, DQ = -0.138az mC/m2, DL = 0.24ax + 0.18 az mC/m2, D = 240ax+42az µC/m2)

Solution

6. A non-conducting ring of radius R with a uniform charge density, D and a total charge Q is lying in the xy-plane, as shown in figure below. Compute the electric field at a point P, located at a distance z from the center of the ring along its axis of symmetry. (Ans:

E z=1

4 π ϵ 0

Q z

(r2+ z2)3/2

Electric field at P due to the charge element dqSolution

7. In the classical model of the hydrogen atom, the electron revolves around the proton with a radius of r = 0.53 x 10-10 m. The magnitude of the charge of the electron and proton is e = 1.6 x 10-19 C.(a) What is the magnitude of the electric of the electric force between the proton and the

electron? (Ans: 8.2 x 10-8 N)(b) What is the magnitude of the electric field due to the proton at r? (Ans: 5.76 x 1011 N/C)(c) What is ratio of the magnitude of the electrical and gravitational force between electron

and proton? Does the result depend on the distance between the proton and the electron? (Ans: 2.2 x 1039 )

(d) In the light of your calculation in (b), explain why electrical forces do not influence the motion of planets.

Solution

8. A non-conducting rod of length, l with a uniform charge density, D and a total charge Q is lying along the x-axis, as illustrated in figure below. Compute the electric field at a point P,

located at a distance, y off the axis of the rod. (Ans: E y=ρ

4 π ε0 y (sin θ2−sinθ1 )

Solution