Slide 1 / 29 Slide 2 / 29 1. Sphere 1 carries a positive charge 1. Sphere 1 carries a positive charge Q = +6 µC and located at the origin. Q = +6 µC and located at the origin. a. What is the direction of the electric field a. What is the direction of the electric field at at point P 0.6 m away from the origin? point P 0.6 m away from the origin? b. What is the magnitude of the electric field at point P? A test charge q = +1 µC and mass m = 2.5 g is to the right brought from infinity and placed at point P c. What is the direction of the electric force on charge q due to charge Q? d. What is the magnitude of the electric force on charge q due to charge Q? e. What is the acceleration of charge q at the instant when it is released from point P? Slide 3 / 29 Slide 4 / 29 1. Sphere 1 carries a positive charge 1. Sphere 1 carries a positive charge Q = +6 µC and located at the origin. Q = +6 µC and located at the origin. A test charge q = +1 µC and mass m = 2.5 g is b. What is the magnitude of the electric brought from infinity and placed at point P field at point P? c. What is the direction of the electric force on charge q due to charge Q? E = kq/r 2 to the right E = (9x10 9 Nm 2 /C 2 )(6x10 -6 C)/(0.6m) 2 E = 1.5x10 5 N/C Slide 5 / 29 Slide 6 / 29 1. Sphere 1 carries a positive charge 1. Sphere 1 carries a positive charge Q = +6 µC and located at the origin. Q = +6 µC and located at the origin. A test charge q = +1 µC and mass m = 2.5 g is A test charge q = +1 µC and mass m = 2.5 g is brought from infinity and placed at point P brought from infinity and placed at point P d. What is the magnitude of the electric force e. What is the acceleration of charge q at the on charge q due to charge Q? instant when it is released from point P? F E = kQq/r 2 or F E = qE ΣF = ma F E = (1x10 -6 C)(1.5x10 5 N/C) a = ΣF/m F E = 0.15N a = (0.15N)/(0.025kg) a = 60 m/s 2
Slide 7 / 29 Slide 8 / 29 2. A negatively charged sphere with charge Q = -20 µC 2. A negatively charged sphere with charge Q = -20 µC is placed on an insulating table a tiny charge q and mass is placed on an insulating table a tiny charge q and mass of m = 3.6 g is suspended at rest above charge Q. The of m = 3.6 g is suspended at rest above charge Q. The distance between the charges is 0.8 m. distance between the charges is 0.8 m. a. What is the direction of the electric field due to a. What is the direction of the electric field due to charge Q at the distance d above charge Q? charge Q at the distance d above charge Q? b. What is the magnitude of the electric field due to charge Q at the distance d above charge Q? c. On the diagram below show all the forces applied on charge q. down d. What should be the sign and magnitude of the charge q in order to keep it at equilibrium? Slide 9 / 29 Slide 10 / 29 2. A negatively charged sphere with charge Q = -20 µC 2. A negatively charged sphere with charge Q = -20 µC is placed on an insulating table a tiny charge q and mass is placed on an insulating table a tiny charge q and mass of m = 3.6 g is suspended at rest above charge Q. The of m = 3.6 g is suspended at rest above charge Q. The distance between the charges is 0.8 m. distance between the charges is 0.8 m. b. What is the magnitude of the electric field due to c. On the diagram below show all the forces applied charge Q at the distance d above charge Q? on charge q. E = kQ/r 2 F E E = (9x10 9 Nm 2 /C 2 )(20x10 -6 C)/(0.8m) 2 E = 2.8x10 5 N/C mg Slide 11 / 29 Slide 12 / 29 3. A charge Q 1 = -32 µC is fixed on the y axis at 2. A negatively charged sphere with charge Q = -20 µC y = 4 m, and a charge Q 2 = +18 µC is fixed on is placed on an insulating table a tiny charge q and mass the x axis at x = 3 m. of m = 3.6 g is suspended at rest above charge Q. The distance between the charges is 0.8 m. a. Calculate the magnitude of the electric field E 1 at the origin due to charge Q 1 d. What should be the sign and magnitude of the charge q in order to keep it at equilibrium? b. Calculate the magnitude of the electric field E 2 at the origin due to charge Q 2 . For the magnitude: ΣF = ma since the charge q is at rest, a = 0... ΣF = 0 c. On the diagram (to the right), draw and label the electric fields E 1 , F E - W = 0 E 2 and the net electric field at the origin. F E = W kQ 1 Q 2 /r 2 = mg d. Calculate the net electric field at the origin due to two charges Q 1 and 2 /kQ 1 Q 2 = mgr Q 2 . 2 )(0.8 m) 2 /(9x10 9 Nm 2 /C 2 )(20x10 -6 C) Q 2 = (0.0036 kg)(9.8 m/s -7 C Q 2 = 1.25x10 Since the charge on the sphere is negative, charge q must be repelled and therefore, Q2 is negative
Slide 13 / 29 Slide 14 / 29 3. A charge Q 1 = -32 µC is fixed on the y axis at 3. A charge Q 1 = -32 µC is fixed on the y axis at y = 4 m, and a charge Q 2 = +18 µC is fixed on y = 4 m, and a charge Q 2 = +18 µC is fixed on the x axis at x = 3 m. the x axis at x = 3 m. a. Calculate the magnitude of the electric field b. Calculate the magnitude of the electric field E 1 at the origin due to charge Q 1 E 2 at the origin due to charge Q 2 . 2 E = KQ 1 / r 1 2 E = KQ 1 / r 1 E = (9x10 9 Nm 2 /C 2 ) (18x10 -6 C 2 ) / (4 m) 2 E = (9x10 9 Nm 2 /C 2 ) (32x10 -6 C) / (3 m) 2 E = 1.8X10 4 N/C E = 1.8X10 4 N/C Slide 15 / 29 Slide 16 / 29 3. A charge Q 1 = -32 µC is fixed on the y axis at 3. A charge Q 1 = -32 µC is fixed on the y axis at y = 4 m, and a charge Q 2 = +18 µC is fixed on y = 4 m, and a charge Q 2 = +18 µC is fixed on the x axis at x = 3 m. the x axis at x = 3 m. d. Calculate the net electric field at c. On the diagram (to the right), the origin due to two charges Q 1 and draw and label the electric fields E 1 , Q 2 . E 2 and the net electric field at the origin. E net E net = E Q1 + E Q2 E Q1 E = (1.8x10 4 ) 2 + (1.8x10 4 ) 2 E Q2 E = 2.5x10 4 N/C Slide 17 / 29 Slide 18 / 29 4. A wall has a negative charge 4. A wall has a negative charge distribution producing a uniform field. A distribution producing a uniform field. A small dielectric sphere of mass 10 g and small dielectric sphere of mass 10 g and charge of -90 µC is attached to one end of charge of -90 µC is attached to one end of insulating string 0.6 m long. The other end insulating string 0.6 m long. The other end of the string is attached to the wall. The of the string is attached to the wall. The uniform electric field has a magnitude of uniform electric field has a magnitude of 500 N/C. 500 N/C. a. What is the direction of the uniform electric field? a. What is the direction of the uniform electric field? b. What is the direction and magnitude of the electric field on charge q due to uniform electric filed? left c. On the diagram below draw and label all the applied forces on charge q. d. Calculate the angle θ between the wall and the string. e. Calculate the shortest distance between the wall and charged sphere. f. The string is cut: i. Calculate the magnitude of the net acceleration of the charged sphere q. ii. Describe the resulting path of the charged sphere.
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