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a a - q +q +q General Physics II – PHYS 1120 Soln Homework ASSIGNMENT III Ch (25) ------------------------------------------------------------------------------ --------------------------------------------------------- Instructor: Dr. Adel Hashish Fall 2012 Student's Name: ID#: ------------------------------------------------------------------------------ --------------------------------------------------------- (All necessary calculations have to be shown) I) Circle the correct answer for the following questions 1- Three charged conducting spheres of different radii are connected by thin metal wires. The electric potential (V) and electric field (E) at the surfaces of the three spheres are such a) V 1 = V 2 = V 3 and E 1 = E 2 = E 3 b) V 1 > V 2 > V 3 and E 1 > E 2 > E 3 c) V 1 = V 2 = V 3 and E 1 > E 2 > E 3 d) V 1 > V 2 > V 3 and E 1 = E 2 = E 3 2- The electrical potential energy (U) of the system of three charges shown in the figure below is: a) k e q 2 2 a b) 2 k e q 2 a c) 3 k e q 2 2 a

3 Soln Practice Assignment Ch25

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Page 1: 3 Soln Practice Assignment Ch25

a a

-q +q+q

General Physics II – PHYS 1120

Soln Homework ASSIGNMENT III Ch (25)

---------------------------------------------------------------------------------------------------------------------------------------

Instructor: Dr. Adel Hashish Fall 2012 Student's Name: ID#: ---------------------------------------------------------------------------------------------------------------------------------------

(All necessary calculations have to be shown)

I) Circle the correct answer for the following questions

1- Three charged conducting spheres of different radii are connected by thin metal wires. The electric potential (V) and electric field (E) at the surfaces of the three spheres are such

a) V1 = V2 = V3 and E1= E2 = E3

b) V1 > V2 > V3 and E1> E2 > E3

c) V1 = V2 = V3 and E1> E2 > E3

d) V1 > V2 > V3 and E1= E2 = E3

2- The electrical potential energy (U) of the system of three charges shown in the figure below is:

a) −

ke q2

2 a

b) −2

ke q2

a

c) 3

ke q2

2a

d)

ke q2

a .

Page 2: 3 Soln Practice Assignment Ch25

3- If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = –3.0 nC in the figure,

what is the potential difference V A−V B ?

a. +60 V b. +72 Vc. +84 Vd. +96 Ve. +48 V

4- Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of 36i N/C at point P. Determine the work required of an external agent to move a 3.0-µC charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle.

a. 21 mJb. 18 mJ c. 24 mJd. 27 mJe. 12 mJ

5- Four identical point charges (+4.0 µC) are placed at the corners of a square which has 20-cm sides. How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges?

a. +2.9 Jb. +3.9 J c. +2.2 Jd. +4.3 Je. +1.9 J

6- A charge of +3.0 µC is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25µC from infinity to the center of the circle?

a. 5.4 Jb. 3.4 J c. 4.3 Jd. 2.7 Je. 6.8 J

Page 3: 3 Soln Practice Assignment Ch25

7- A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points?

a. 23 Vb. 30 V c. 15 Vd. 45 Ve. 60 V

8- A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away?

a. 12 Vb. 6.8 Vc. 3.0 V d. 4.7 Ve. 2.2 V

9- Equipotentials are lines along whicha. the electric field is constant in magnitude and direction.b. the electric charge is constant in magnitude and direction.c. maximum work against electrical forces is required to move a

charge at constant speed.d. a charge may be moved at constant speed without work

against electrical forces.e. charges move by themselves.

Page 4: 3 Soln Practice Assignment Ch25

Problem 1Calculate the electric potential at point P on the axis of the annulus shown in the figure, which has a uniform charge density σ.

Soln

where

Problem 2Two parallel plates having charges of equal magnitude but opposite sign are separated by 12.0 cm. Each plate has a surface charge density of 36.0 nC/m2. A proton is released from rest at the positive plate. Determine

(a) the potential difference between the plates, (b) the kinetic energy of the proton when it reaches the negative plate, (c) the speed of the proton just before it strikes the negative plate, (d) the acceleration of the proton, and (e) the force on the proton. (f) From the force, find the magnitude of the electric field and show that it is equal to the electric field found from the charge densities on the plates.

Soln

The positive plate by itself creates a field away from the + plate. The negative plate by itself creates the same size field and between the plates it

Page 5: 3 Soln Practice Assignment Ch25

is in the same direction. Together the plates create a uniform field in the space between.

(a) Take at the negative plate. The potential at the positive plate is then

.

The potential difference between the plates is

.

(b)

(c)

(d)

(e)

(f)

Problem 3Three charges Q1 = 16 μC, Q2 = 10 μC, and Q3 = -9 μC are located on the circumference of a rectangular of length and width 4m and 3m respectively as shown in the figure below.

1- Find the electrical field at point P? 2- What is the electrical potential at P?3- Calculate the work needed to bring a charge Q4 = 10 μC from infinity to point P? 4- Calculate the energy of the system of the four charges?

PQ1

4 m

Page 6: 3 Soln Practice Assignment Ch25

P (30cm, 0)x

Rx

y

Q

Soln

Problem 4A uniformly charged insulating sphere, of radius R = 15 cm, having a negative charge Q = -5.3 C. A positive point charge q1 = 4.2 C is placed at point (x = 30 cm, y = -20 cm) as shown in the figure below. A point P is located on the x-axis at a distance x = 30 cm from the origin. Note that the center of the sphere coincides with the origin of the coordinates axes. a) Find the electric field (magnitude and direction) at point P.

b) Find the electric potential at point P.

c) What is the energy needed to bring a point charge q2 = -3.6 C from infinity to place it at the point P?

d) Find the total electric force (magnitude and direction) on the point charge q2.

Q2 Q3

3 m

q1 (30cm, -20cm)

Page 7: 3 Soln Practice Assignment Ch25

Soln: