Physics 72: Chapter 21 Problem Set

Summer 2010

Name: Date: Lecturer: Mr Carlos Baldo III Section: X7-7 Instructions: Solve each problem CONSCIENTIOUSLY. In calculations, use the available spaces. 1.

Charging. Three identical metallic spheres with charges 9 C, 7 C and 5 C, are placed in contact with each other and pulled apart after electrostatic equilibrium is reached. What will be the final charge of each sphere? Let e = 1.67 x 10-19. A. 9 C, 7 C, 5 C B. 5 C, 7 C, 9 C C. 0 C, 0 C, 0 C D. 7 C, 7 C, 7 C E. e C, e C, e C

2.

Charging. A negatively charged rod is placed near but not touching an isolated uncharged insulating sphere. The far side of the insulator with respect to the rod is then connected to the ground. After reaching equilibrium, the connection to ground is removed. What would be the charge of the sphere after the rod is removed? A. Positive B. Negative C. Uncharged D. It depends on the separation distance between the rod and sphere E. It depends on the size of the sphere

3.

Coulomb’s Law. The lengths of the arrow, representing the INDIVIDUAL forces, are equal. i) Assign the charges so that these forces are correct (write either + or – inside the circles). ii) Draw broken arrows (---) to represent the NET forces on each charge due to other charges. There are two possible cases. Consider one using the figure on the left and another case on the right.

4.

Coulomb force. A q1 = 6-C and a q2 = 3-C charge are separated by some distance. If the magnitude of the Coulomb force acting on q2 due to the q1 is 2 × 10-9 N, what is the magnitude of the force acting on q1 due to q2? A. 1 × 10-9 N B. 2 × 10-9 N C. Zero D. - 1 × 10-9 N E. - 2 × 10-9 N

5.

Electric Force. A negative charge (test charge) is placed on the position marked by the X. Which of the following arrow best describes the force vector on the test charge?

Physics 72: Chapter 21 Problem Set

Summer 2010

6.

Coulomb’s Law. Three charges lie on the x-axis: q1=+20nC at the origin, q2 =–12nC at x =2m, q3=+18nC at x =3 m. What is the magnitude of the net electric force on q1? Let k = 1/(4пε0) ≈ 9 x 109Nm2/C2. A. zero B. 1.8 x 10-7 N C. 3.6 x 10-7 N q3 q2 q1 D. 5.4 x 10-7 N E. 9.0 x 10-7 N 2m 1m

7.

Force and test charge. Electric charge is distributed uniformly along each side of a square. Two adjacent sides have total charge +Q on each while the other sides have total charge -Q. What is the direction of the net force acting on a 7Q point charge at the origin? A. Towards the first quadrant B. Towards the second quadrant C. Towards the third quadrant D. Towards the fourth quadrant E. Zero

8.

Electric fields. The electric field at the location of a charge q is given by E. What would be the electric field if charge is replaced by q/2? A. E/4 D. 2E B. E/2 E. 4E C. E

9.

Electric fields. Charge Q is placed at Point X. There, it detected an electric field given by E. If charge Q is replaced by Q/2, what would be the electric force on Q/2? D. 2QE A. QE/4 E. 4QE B. QE/2 C. QE

10. Coulomb’s Law. A -5C charge placed in a region with a uniform electric field, experiences an electric force equal to (45N)i. If this charge is replaced by a +7C charged ball, what is electric force on the ball? A. - (7N)i B. - (36N)i C. - (45N)i D. - (63N)i E. - (315N)i 11. Coulomb’s Law. What is the Coulomb force acting on a -3-C point charge if the electric field at its location is (5 i – 3 j) N/C? A. (-5 i + 3 j) N B. (-15 i + 9 j) N C. Zero D. (5 i – 3 j) N E. (15 i – 9 j) N 12. Electric fields. Two charges are placed on two corner of a square. Which arrow best represents the direction of the net electric field at the corner indicated as Point P? 13. Electric fields and test charges. A +3-μC test charge is placed at point P where the electric field due to other charges is directed to the right and has a magnitude of 4 x 106 N/C. If the test charge is replaced with a charge of -3μC, the electric field due to other charges at point P A. remains the same. B. increases in magnitude and changes direction. C. decreases in magnitude and changes direction. D. has the same magnitude as before, but changes direction. E. None of these.

Physics 72: Chapter 21 Problem Set

Summer 2010

14. Electric field. What is the electric field acting on a -2C point charge if it detects an electric force of (14i – 6j) N? A. (14 i – 6 j) N /C B. (-7 i + 3 j) N/C C. √2(14 + 6)(i – j) N /C D. 2(142 + 62)1/2 (i – j) N /C E. -2(142 + 62)1/2 (i – j) N /C 15. Electric fields and test charges. Two infinite plane sheets of surface charge density σ > 0 are placed parallel to each other, separated by a distance d. What is the magnitude of the force acting on a point charge 2q placed a distance x from the far side of one of the sheets? A. 2qσ/ε0 B. 2qσx/ε0 C. qσ/ε0 D. qσx/ε0 E. Zero 16. Electric field. Two point charges were released from the same location and with the same velocity towards a uniform electric field. Their trajectories are shown in the figure. What can be said of the two charges? A. A is positive and heavier than B B. B is positive and heavier than A C. A is negative and heavier than B D. B is negative and heavier than A E. None of the above is true 17. Electric fields. Charges are placed on the corner of a square of side 2d as shown in the figure. What is the magnitude of the electric field at the center of the square? A.

−

kq 2 2d

D.

B.

−

E.

C.

kq d2

Zero

kq d2 kq 2d2

18. Electric Dipole. Consider 5 isolated electric diploes whose dipole moment vectors are shown. If these dipoles are immersed in a uniform electric field directed into the page, which of these dipoles would be in a stable equilibrium?

19. Electric fields and test charges. An electric dipole, with dipole moment p, consists of two charges +q and -q separated by a very small distance 2a. Its center is on the x axis at x = x1, and p points in the positive x direction. The dipole is in a nonuniform electric field, which is also in the x direction, given by E = Cxi, where C is a constant. Find the net force on the dipole. A. 2Cqx1 i B. -2Cqx1 i C. Zero D. –Cp E. Cp