Q(2, 1, 4) toward P(1, 2, 3): A little thought is in order here: Note that the field has only
a radial component and does not depend on φ or z. Note also that P and Q are at the
same radius (√5) from the z axis, but have different φ and z coordinates. We could just
as well position the two points at the same z location and the problem would not change.
If this were so, then moving along a straight line between P and Q would thus involve
moving along a chord of a circle whose radius is √5. Halfway along this line is a point of
symmetry in the field (make a sketch to see this). This means that when starting from
either point, the initial force will be the same. Thus the answer is dW = 3.1 µJ as in part
a. This is also found by going through the same procedure as in part a, but with the
direction (roles of P and Q) reversed.
Q(2, 1, 4) toward P(1, 2, 3): A little thought is in order here: Note that the field has onlya radial component and does not depend on φ or z. Note also that P and Q are at thesame radius (√5) from the z axis, but have different φ and z coordinates. We could justas well position the two points at the same z location and the problem would not change.If this were so, then moving along a straight line between P and Q would thus involvemoving along a chord of a circle whose radius is √5. Halfway along this line is a point ofsymmetry in the field (make a sketch to see this). This means that when starting fromeither point, the initial force will be the same. Thus the answer is dW = 3.1 µJ as in parta. This is also found by going through the same procedure as in part a, but with thedirection (roles of P and Q) reversed.
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