Physics 9 Page 1 WS E2 (rev. 1.0) E-2. Electric fields Summary An electric force requires two charges. An electric field is produced by a single charge. Questions for discussion 1. Sketch the electric field created by each of the following point charges. a) q = +1 C +1 b ) q = -2 C -2 2. A long straight piece of fishing line has been sprayed evenly with positively charged paint. This creates a uniform line charge distribution (as opposed to a point charge). Sketch the electric field created by this line of charge. + + + + + + + + + + + + + + perspective view side view end view How would your picture look if the line were negatively charged? 3. Next, a large sheet of plastic has been sprayed evenly with positively charged paint. (See figure next page.) This creates a uniform surface charge distribution. Sketch the electric field created by this surface charge. Physics 9 Page 2 WS E2 (rev. 1.0) + + + + + + + + + + + + + + + + + + + + + + + +e + + + + + + + + + + + + + + + perspective view side view face view (surface charge suppressed) How would your picture look if the sheet were negatively charged? 4. This time, two charged sheets are placed near each other. One has uniform positive surface charge, while the other has uniform negative surface charge. Sketch the (net) electric field created by the sheets. - + + + + + + + + + + side view perspective view 5. Repeat Discussion Question 4 if the sheets are both positively charged. + + + + + + + + + + + + + + + + + + side view Physics 9 Page 3 WS E2 (rev. 1.0) Problems 1. Two point charges q1 = +3 C and q2 = -3 C are fixed in place, as shown. They are separated by 0.4mm, and are centered at the origin. a) Is the electric field due to q1 and q2 at the origin zero? If so, explain why. If not, find the magnitude of the electric field at the origin. b ) What is the magnitude of the electric field at point A, at y = -0.5 mm? y c ) What is the magnitude of the electric field at y = +0.5 mm? d) What is the magnitude of the electric field at point B, at x = -0.5 mm? C +3 C 0.2 mm x B 0.2 mm -3 C e ) Is there any location at which the electric field created by the point charges q1 and q2 is zero? f) A The points A, B, and C in the figure are not point charges. They are merely locations in the x-y plane. 2. Three point charges are equidistant from one another and fixed in place. a) Sketch the net electric field vector at the center of the triangle. b ) Calculate the electric field at this point. Sketch qualitatively the electric field lines due to q1 and q2. Physics 9 Page 4 WS E2 (rev. 1.0) 3. A point mass m with positive charge q is suspended from the ceiling by a thread. Nearby, a charged object causes the point charge q to deflect from the vertical. Our task will be to find the angle of deflection in various cases. (Refer to Table at right.) c ) Finally, suppose that the nearby object is a long positively charged line, with uniform linear charge density λ, located a horizontal distance D away. a) First suppose that the nearby object is another positive point charge Q, located a horizontal distance D away. Find the angle of deflection θ. Electric fields created by various charged objects Find the angle of deflection θ. b ) Next suppose that the nearby object is a large positively charged sheet, with uniform surface charge density σ, located a perpendicular distance D away. Shape of charged object Point charge Q Infinite straight line of charge, uniform linear charge density λ Find the angle of deflection θ. Infinite flat sheet of charge, uniform surface charge density σ Strength of E-field created by object E (r ) = E (r ) = Q 4πε0 r2 Note “r” refers to distance from the point charge. λ 2πε0r “r” refers to perpendicu-lar distance from the line charge. σ 2ε 0 E-field strength is independent of distance from the sheet. E (r ) = Physics 9 Page 5 WS E2 (rev. 1.0) 4 . A thin rod of length L and uniform positive charge per unit length −λ is positioned on the x–axis with one end at x = d. A second rod, also of length L but with uniform charge per unit length +λ, is positioned with one end at x = –d. 5 . A semicircle of radius R has charge +q spread uniformly on it. a) Sketch the electric field vector at point P. your reasoning. Explain b ) Find the strength of the electric field at point P. Find the electric field at the origin O (x = 0). If the electric field is zero at this point, explain why. Otherwise find both the magnitude and direction of the field at the origin.