AP Physics – Electrostatics Examples

 

1.      Point charge q1 = 3.0 nC is located at the origin and point charge q2 = -4.0 nC is located at (2.0 m, 0).  (a) Determine the force on q1.  (b) Determine the force on q2.

2.      Point charge q1 = 5.0 nC is located at the origin and point charge q2 = -5.0 nC is located at (0, 3.0 m).  Determine the net force on a third point charge q3 = 2.0 nC if it is located at:  (a) (0, 2.0 m),  (b) (2.0 m, 0), or (c) (2.0 m, 1.5 m).

3.      A charged pith ball of mass 0.15 g dangles from a string and is attracted to a sphere with charge −2.0 μC.  It “floats” in equilibrium with the string tilted 20.0° from vertical when located 0.40 m from the center of the sphere.  (a) Find the charge on the pith ball.  (b) Find the number of excess or deficit electrons on the pith ball.

4.      Find the electric force and the gravitational force between the proton and electron in a hydrogen atom.  The radius of the atom is 5.3 × 10−11 m.

5.      Find the electric force and the gravitational force between the two protons in the nucleus of a helium atom.  The protons are separated by 1 × 10−15 m.

6.      Two oppositely charged point objects, −q1 and q2 are separated by distance a.  The two charges are unequal amounts such that |−q1| > |q2|.  Determine an expression for the position at which a third point charge could be placed and experience a net electrostatic force of zero.

7.      Three point charges are situated in the form of an equilateral triangle with sides of length a.  (a) If all three charges are equal to q, determine the net force on any one of the three.  (b) If one of the charges is −q and the others are each q, determine the net force on each.

8.      A thin rod of length L has a uniform charge Q.  Determine the force on a point charge q located a distance d from one end of the rod (along the axis of the rod).

9.      An “electron gun” produces an electric field of 90.0 kN/C in a region between two parallel metal plates separated by 0.50 cm.  (a) Determine the amount of force acting on the electron (q = 1.602 × 10-19 C, m = 9.11 × 10-31 kg).  (b) Determine the acceleration of the electron.  (c) Determine the speed acquired by the electron assuming it starts from rest at one plate.  (d) Repeat for a proton (m = 1.67 × 10-27 kg ) “fired” by the same “gun”.

10.  A uniform electric field of 150 N/C downward exists near the surface of the Earth.  Suppose an electron is “launched” from the end of a TV picture tube with a horizontal speed 2.0 × 107 m/s and travels a horizontal distance of 20.0 cm before impacting the screen.  (a) Determine the acceleration of the electron due to the earth’s field.  (b) Determine the vertical deflection that occurs before the electron hits the screen.

11.  Suppose that an oil drop in Millikan’s experiment is observed to fall with a terminal velocity of 0.250 mm/s in the presence of air resistance of F = -kv, where k = 1.60 × 10-10 kg/s.  This drop is then subjected to a downward electric field of 1.00 × 105 N/C and observed to rise with a terminal velocity of 0.0500 mm/s.  (a) Determine the mass of the oil drop.  (b) Determine the charge on the oil drop.  (c) How many excess electrons are on the drop?

12.  Seventeen equal point charges q are arranged in a circle of radius R.  The charges are equally spaced along the circumference.  If one of the point charges is removed, what is the electric field at the center of the circle due to the presence of the remaining sixteen charges?

13.  Consider a line of charge with length L and uniform charge Q.  Determine the electric field at a distance r along a perpendicular bisector.

14.  Consider a thin ring of radius R and uniform charge Q in the xy plane.  Determine the electric field a distance z along the axis of the ring.

15.  Consider a thin disk of radius R and uniform charge Q in the xy plane.  Determine the electric field a distance z along the axis of the disk.

16.  Consider a thin ring of radius R and uniform charge Q in the xy plane centered on the origin.  Determine the electric field as a function of x.

 

 

 

Answers

 

1.      a. 2.7 ´ 10-8 N, 0°
b. 2.7 ´ 10-8 N, 180°

2.      a. 1.1 ´ 10-7 N, 90°
b. 1.9 ´ 10-8 N, 17°
c. 1.7 ´ 10-8 N, 90°

3.      a. 4.8 nC
b. deficit of 30 billion electrons

4.      8.2 × 10−8 N, 3.6 × 10−47 N

5.      230 N, 1.8 × 10−34 N

6.       on the side of q2 opposite from the other charge

7.      a. on each:  away from the center of the triangle
b. on -q:   toward the center of the triangle
    on each q:   parallel to the opposite side

8.     

9.      a. 1.44 × 10-14 N
b. 1.58 × 1016 m/s2 opposite field
c. 13 Mm/s
d. 1.44 × 10-14 N, 8.63 × 1012 m/s2 in direction of field, 290 km/s

10.  a. 2.6 × 1013 m/s2
b. 1.3 mm upward

11.  a. 4.08 × 10-15 kg
b. 4.80 × 10 -19 C
c. 3.0

12.  kq/R2 away from center, toward missing charge

13.   perpendicular to line of charge

14.   along the axis

15.   along the axis

16.   along the x-axis