Electric Field Lines: Multiple Charges Quiz

PDF page 865: In many situations, there are multiple charges. The total electric field created by multiple charges is the vector sum of the individual fields created by each charge. The following example shows how to add electric field vectors.

PDF page 864: charge. Drawings using lines to represent electric fields around charged objects are very useful in visualizing field strength and direction. Since the electric field has both magnitude and direction, it is a vector. Like all vectors, the electric field can be represented by an arrow that has length proportional to its magnitude and that points in the correct direction. (We have used arrows extensively to represent force vectors, for example.)

PDF page 864: magnitude and direction. (b) In the standard representation, the arrows are replaced by continuous field lines having the same direction at any point as the electric field. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have a strength proportional to the density of the lines (being greater near the charge, for example). Note that the electric field is defined for a positive test charge , so that the field lines point away from a positive charge and toward a negative charge. (See Figure 18.28.) The electric field strength is exactly proportional to the number of field lines per unit area, since the magnitude of the electric field for a point charge is and area is proportional to . This pictorial representation, in which field lines represent the direction and their

PDF page 864: magnitude and direction. (b) In the standard representation, the arrows are replaced by continuous field lines having the same direction at any point as the electric field. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have a strength proportional to the density of the lines (being greater near the charge, for example). Note that the electric field is defined for a positive test charge , so that the field lines point away from a positive charge and toward a negative charge. (See Figure 18.28.) The electric field strength is exactly proportional to the number of field lines per unit area, since the magnitude of the electric field for a point charge is and area is proportional to . This pictorial representation, in which field lines represent the direction and their

PDF page 866: representative points and drawing electric field lines consistent with those points. While the electric fields from multiple charges are more complex than those of single charges, some simple features are easily noticed. For example, the field is weaker between like charges, as shown by the lines being farther apart in that region. (This is because the fields from each charge exert opposing forces on any charge placed between them.) (See Figure 18.30 and Figure 18.31(a).) Furthermore, at a great distance from two like charges, the field becomes identical to the field from a single, larger charge.

PDF page 866: representative points and drawing electric field lines consistent with those points. While the electric fields from multiple charges are more complex than those of single charges, some simple features are easily noticed. For example, the field is weaker between like charges, as shown by the lines being farther apart in that region. (This is because the fields from each charge exert opposing forces on any charge placed between them.) (See Figure 18.30 and Figure 18.31(a).) Furthermore, at a great distance from two like charges, the field becomes identical to the field from a single, larger charge.

PDF page 866: representative points and drawing electric field lines consistent with those points. While the electric fields from multiple charges are more complex than those of single charges, some simple features are easily noticed. For example, the field is weaker between like charges, as shown by the lines being farther apart in that region. (This is because the fields from each charge exert opposing forces on any charge placed between them.) (See Figure 18.30 and Figure 18.31(a).) Furthermore, at a great distance from two like charges, the field becomes identical to the field from a single, larger charge.

PDF page 866: Figure 18.31(b) shows the electric field of two unlike charges. The field is stronger between the charges. In that

PDF page 866: region, the fields from each charge are in the same direction, and so their strengths add. The field of two unlike charges is weak at large distances, because the fields of the individual charges are in opposite directions and so their strengths subtract. At very large distances, the field of two unlike charges looks like that of a smaller single charge.

PDF page 864: magnitude and direction. (b) In the standard representation, the arrows are replaced by continuous field lines having the same direction at any point as the electric field. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have a strength proportional to the density of the lines (being greater near the charge, for example). Note that the electric field is defined for a positive test charge , so that the field lines point away from a positive charge and toward a negative charge. (See Figure 18.28.) The electric field strength is exactly proportional to the number of field lines per unit area, since the magnitude of the electric field for a point charge is and area is proportional to . This pictorial representation, in which field lines represent the direction and their

PDF page 864: individual arrows with each arrow representing the force on a test charge . Field lines are essentially a map of infinitesimal force vectors.

PDF page 864: magnitude and direction. (b) In the standard representation, the arrows are replaced by continuous field lines having the same direction at any point as the electric field. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have a strength proportional to the density of the lines (being greater near the charge, for example). Note that the electric field is defined for a positive test charge , so that the field lines point away from a positive charge and toward a negative charge. (See Figure 18.28.) The electric field strength is exactly proportional to the number of field lines per unit area, since the magnitude of the electric field for a point charge is and area is proportional to . This pictorial representation, in which field lines represent the direction and their