Question

A negatively charged object is located in a region of space where the electric field is uniform and points due north. the object may move a set distance d to the north, east, or south. rank the three possible movements by the change in electric potential energy (ue) of the object. rank from greatest increase to decrease in ue.

Answer 1

- The largest increase in potential energy occurs when the charge is moving north. This is because the charge is negative, so it acquires potential energy when moving in the same direction of the field (viceversa, a positive charge when moving in the direction of the field it loses potential energy converting it into kinetic energy). The amount of potential energy gained is equal to the product of the charge and the distance covered:
$\Delta U = e d$

- The second largest increase is when the charge is moving east. In this case, actually, the variation of potential energy is zero. This is because the charge is moving perpendicular to the field, and so it is moving along points with same potential. Therefore, in this case the variation of potential energy is zero:
$\Delta U = 0$

- Finally, when the charge is moving south, it loses potential energy. This is because it is moving against the electric field, and since it is a negative charge, in this direction it loses potential energy converting it into kinetic energy. Therefore, in this case:
$\Delta U = - e d$

Answer 2

(a) There will be an increase in the potential energy when the charge moves North.

(b) The variation of potential energy will be zero when the charge is moving to the east.

(c)There is a loss in potential energy when a charge moves to the South.

What will be the potential energy of the charge at different directions?

(a) The largest increase in potential energy occurs when the charge is moving north. This is because the charge is negative,

so it acquires potential energy when moving in the same direction of the field (vice versa, a positive charge when moving in the direction of the field loses potential energy converting it into kinetic energy).

The amount of potential energy gained is equal to the product of the charge and the distance covered:

$\rm \Delta PE=qD$

(b) The second-largest increase is when the charge is moving east. In this case, actually, the variation of potential energy is zero.

This is because the charge is moving perpendicular to the field, and so it is moving along points with the same potential. Therefore, in this case, the variation of potential energy is zero:

$\rm \Delta PE=0$

(c) Finally, when the charge is moving south, it loses potential energy. This is because it is moving against the electric field,

since it is a negative charge, in this direction it loses potential energy converting it into kinetic energy. Therefore, in this case

$\rm \Delta PE=-qD$

Thus

(a) There will be an increase in the potential energy when the charge moves North.

(b) The variation of potential energy will be zero when the charge is moving to the east.

(c)There is a loss in potential energy when a charge moves to the South.

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