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# Direction and Work Done by Electric Field

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4 a) Sketch arrows on the diagram (see attachment) to indicate the direction of the electric field, if any, at each of the points A, B, C, and D.

A positively charged test particle is observed to move as described below. For each motion, tell whether the work done by the electric field is positive, negative, or zero. Explain your reasoning in each case. Two charges +Q and -Q are fixed in place at the positions shown. Four points A, B, C, and D are labeled on the diagram.

b)

? The test charge moves from point B to point A

? The test charge moves from point B to point C

? The test charge moves from point B to point D

c) Rank, from highest to lowest, the electric potentials at points A, B, C and D. Explain.

5. For each pair of charges, draw a force vector on each charge to show the electric force acting on that charge. The length of each vector should be proportional to the magnitude of the force. Each (+) and (-) symbol represents the same quantity of charge.

6. (10 pts.) For each of the figures, use dots to mark any point or points (other than infinity) where the electric field is zero. Explain your reasoning for part (a).

https://brainmass.com/physics/scalar-and-vector-operations/direction-work-done-electric-field-65255

#### Solution Preview

SOLUTION

a) By definition electric field (intensity) at a point is the force experienced by a unit positive charge placed at that point. Let us take each point and see in which direction a unit positive charge placed at that point will experience the resultant force due to two charges.

Point A : Unit positive charge will experience attraction from -Q charge and repulsion from +Q charge. Thus. both charges are pushing it towards -Q charge and the resultant force is towards the charge -Q. The direction of electric field will be towards -Q charge.

Points B,C : In fact, the resultant force experienced by a unit positive charge will be towards -Q charge wherever it may be placed on the straight line joining the two charges. Thus, the direction of electric field at C and D will also be towards -Q charge.

Point D : To find the direction of electric field at D, we have to add the forces experienced by the unit positive charge placed at that point as shown in the fig.. The thin arrows indicate the individual forces due to the charges and the thick arrow the direction of the resultant i.e. the direction of electric field .

b) By definition, work done by a force is defined as :
Work done = Component of the force in ...

#### Solution Summary

Problems on electrostatics solved step by step to highlight the fundamentals. The directions and work done by electric fields are discussed.

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