## Mastering Physics Solutions: Visualizing Electric Fields

Visualizing Electric Fields

Part A = Option D
Part B = Field lines cannot cross each other, The field lines should be parallel because of the sheet’s symmetry
Part C = Option B
Part D = The field lines should be smooth curve, The field lines should always end on negative charges or at infinity
Part E = QA = +7q, QB = -3q

Solution Below:

Electric field lines are a tool used to visualize electric fields. A field line is drawn beginning at a positive charge and ending at a negative charge. Field lines may also appear from the edge of a picture or disappear at the edge of the picture. Such lines are said to begin or end at infinity. The field lines are directed so that the electric field at any point is tangent to the field line at that point.

The figure shows two different ways to visualize an electric field. On the left, vectors are drawn at various points to show the direction and magnitude of the electric field. On the right, electric field lines depict the same situation. Notice that, as stated above, the electric field lines are drawn such that their tangents point in the same direction as the electric field vectors on the left. Because of the nature of electric fields, field lines never cross. Also, the vectors shrink as you move away from the charge, and the electric field lines spread out as you move away from the charge. The spacing between electric field lines indicates the strength of the electric field, just as the length of vectors indicates the strength of the electric field. The greater the spacing between field lines, the weaker the electric field. Although the advantage of field lines over field vectors may not be apparent in the case of a single charge, electric field lines present a much less cluttered and more intuitive picture of more complicated charge arrangements.

Part A

Which of the following figures correctly depicts the field lines from an infinite uniformly negatively charged sheet? Note that the sheet is being viewed edge-on in all pictures.

Option D

Part B

In the diagram from part A , what is wrong with figure B? (Pick only those statements that apply to figure B.)
Check all that apply.

• Field lines cannot cross each other.
• The field lines should be parallel because of the sheet’s symmetry.
• The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance.
• The field lines should always end on negative charges or at infinity.

Field lines cannot cross each other, The field lines should be parallel because of the sheet’s symmetry

Part C

Which of the following figures shows the correct electric field lines for an electric dipole?

Option B

Part D

In the diagram from part C , what is wrong with figure D? (Pick only those statements that apply to figure D.)
Check all that apply.

• Field lines cannot cross each other.
• The field lines should turn sharply as you move from one charge to the other.
• The field lines should be smooth curves.
• The field lines should always end on negative charges or at infinity.

The field lines should be smooth curve, The field lines should always end on negative charges or at infinity

Part E

In the figure, the electric field lines are shown for a system of two point charges, QA and QB. Which of the following could represent the magnitudes and signs of QA and QB?
In the following, take q to be a positive quantity.

• QA = +q, QB = -q
• QA = +7q, QB = -3q
• QA = +3q, QB = -7q
• QA = -3q, QB = +7q
• QA = -7q, QB = +3q

QA = +7q, QB = -3q