HW2solutions - Physics 213 HW #2 Solutions Spring 2008...

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Physics 213 HW #2 – Solutions Spring 2008 21.59. [E-Field Lines & Particle Paths] 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, so the force, (and therefore acceleration and velocity) are always in a straight line in that same direction. The particle moves along the straight field line with increasing speed. In Fig.21.29b the field lines are curved. As the particle moves, its acceleration changes direction due to the changing direction of the electric field and therefore force. The particle’s velocity and acceleration are not in the same direction, and its 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. A gravitational analog: one body in a circular orbit around another has its velocity always perpendicular to acceleration, and a trajectory always perpendicular to the (gravitational) field line. 21.61. [Infinite Line Charge E-Field Lines] (a) IDENTIFY and 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: (b) EXECUTE and EVALUATE: Consider a circle of radius r with the line of charge passing through the center. The spacing of field lines, which represents the magnitude of E, is the same all around the circle. For a different r the spacing would change, so the magnitude of E clearly depends on r. A smaller r would result in a closer spacing, which corresponds to larger E, so E is inversely proportional r. In the direction perpendicular to the plane of the circle the lines are equally spaced, so E does not depend on the position along the line, but rather only on the distance r . The total 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) of the circle. Hence E is proportional to 1/ r . 21.89. [Finite Line of Charge] IDENTIFY: Divide the charge distribution into infinitesimal segments of length dx. Calculate E x due to a segment and integrate to find the total field.
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HW2solutions - Physics 213 HW #2 Solutions Spring 2008...

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