631_PartUniversity Physics Solution

631_PartUniversity Physics Solution - 21-24 Chapter 21...

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21-24 Chapter 21 21.59. IDENTIFY: The force on the particle at any point is always tangent to the electric field line at that point. SET UP: The instantaneous velocity determines the path of the particle. EXECUTE: In Fig.21.29a the field lines are straight lines so the force is always in a straight line and velocity and acceleration are always in the same direction. The particle moves in a straight line along a field line, with increasing speed. In Fig.21.29b the field lines are curved. As the particle moves its velocity and acceleration are not in the same direction and the trajectory does not follow a field line. EVALUATE: In two-dimensional motion the velocity is always tangent to the trajectory but the velocity is not always in the direction of the net force on the particle. 21.60. IDENTIFY: The field appears like that of a point charge a long way from the disk and an infinite sheet close to the disk’s center. The field is symmetrical on the right and left. SET UP: For a positive point charge, E is proportional to 1/ r 2 and is directed radially outward. For an infinite sheet of positive charge, the field is uniform and is directed away from the sheet. EXECUTE: The field is sketched in Figure 21.60. EVALUATE: Near the disk the field lines are parallel and equally spaced, which corresponds to a uniform field. Far from the disk the field lines are getting farther apart, corresponding to the 1/ r 2 dependence for a point charge. Figure 21.60 21.61. IDENTIFY: Use symmetry to deduce the nature of the field lines. (a) SET UP: The only distinguishable direction is toward the line or away from the line, so the electric field lines are perpendicular to the line of charge, as shown in Figure 21.61a. Figure 21.61a (b) EXECUTE and EVALUATE: The magnitude of the electric field is inversely proportional to the spacing of the field lines. Consider a circle of radius r with the line of charge passing through the center, as shown in Figure 21.61b. Figure 21.61b The spacing of field lines is the same all around the circle, and in the direction perpendicular to the plane of the circle the lines are equally spaced, so E depends only on the distance r . The number of field lines passing out through the circle is independent of the radius of the circle, so the spacing of the field lines is proportional to the reciprocal of the circumference 2 r π of the circle. Hence E is proportional to 1/ r . 21.62. IDENTIFY: Field lines are directed away from a positive charge and toward a negative charge. The density of field lines is proportional to the magnitude of the electric field. SET UP: The field lines represent the resultant field at each point, the net field that is the vector sum of the fields due to each of the three charges. EXECUTE: (a) Since field lines pass from positive charges and toward negative charges, we can deduce that the top charge is positive, middle is negative, and bottom is positive.
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631_PartUniversity Physics Solution - 21-24 Chapter 21...

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