Name: ______

Electric Fields and Dipoles – Practice

1. The electric field lines on the left have twice the separation of those on the right.

A. If the magnitude of the field at A is 40 N/C, what is the magnitude of the force on a proton at A?

B. What is the magnitude of the field at B?

2. The nucleus of a plutonium-239 atom contains 94 protons. Assume that the nucleus is a sphere with radius 6.64 fm and with the charge of the protons uniformly spread through the sphere. At the nucleus surface, what are the magnitude and direction (radially inward or outward) of the electric field produced by the protons?

3. Two particles are attached to an x axis: particle 1 of charge -2.00 × 10-7 C at x = 6.00 cm, particle 2 of charge +2.00 × 10-7 C at x = 21.0 cm. Midway between the particles, what is their net electric field in unit-vector notation?

4. Two charged particles are on the x axis: -q = -3.20 × 10-19 C at x = -3.00 m and q = 3.20 × 10-19 C at x = +3.00 m. What are the magnitude and direction (relative to the positive direction of the x axis) of the net electric field produced at point P at y = 4.00 m?

5. An uneven arrangement of electrons (e) and protons (p) exists on a circular arc of radius r = 2.00 cm, with angles θ1 = 30.0°, θ2 = 50.0°, θ3 = 30.0°, and θ4 = 20.0°. What are the magnitude and direction (relative to the positive direction of the x axis) of the net electric field produced at the center of the arc?

Solutions: 1. A. 6.4 x 10-18 N to left B. 20 N/C 2. 3.07 x 1021 N/C radially outward

3. 4. 1.38 x 10-10 N/C to left 5. 3.93 x 10-6 N/C @ -76.4o

Examples Of Finding Electric Fields With Integration

I. Key Equation:

E =

II. Problems

A. Uniformly Charged Rod

1. Linear charge density: l = [ ]

2. dq = ______[ C ]

3. Suggest a material that this rod could be made from: ______

4. Find the electric field at point P.

B. Uniformly Charged Circular Arc

1. Linear charge density: l = ______[ ]

2. dq = ______= ______[ ]

3. E = and . Why?

4. E = = =

C. Uniformly Charged Disk

1. Surface charge density: s = ______[ ]

2. dA = ______

3. Find the area of the circle using A =

4. dq = ______[ C ]

5. What is the direction of the electric field very near the surface of the disk? (The disk is seen edge on it the figure below.)

6. What is the direction of the electric field very far from the disk (i.e outside of the dotted lines)?

D. Uniformly Charged Sphere

A nonconducting sphere of radius R contains a total charge of Q distributed uniformly throughout its volume (e.g. its volume charge density r is constant).

1. Volume charge density: r = ______[ ]

2. dV = ______

3. Find the volume of the sphere using V =

4. dq = ______[ C ]

5. What is the enclosed charge Qenclosed (i.e. the charge inside the radius r) in terms of the total charge Q.

6. What is the magnitude of the electric field at a radius r when r =R in terms of the total charge Q?

7. What is the magnitude of the electric field at a radius r when r =R in terms of the charge density r ?

8. What is the magnitude of the electric field at a radius r when r R?

9. Draw the graph of E versus r that includes the field both the inside and outside.