Problem: A charge of 21 Coulombs moves a distance 84 m, parallel to and opposite to the direction of the field, in an electric field of 18 N/C. How much work is required?
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Solution: The magnitude of the force on a charge of 21 C in a field of strength 18 N/C is 21 C ( 18 N/C) = 378 N. To move the charge parallel to and oppsite to the direction of the field requires that this force be exerted in the direction of motion. Therefore the work will be positive, and will be equal to the product of the magnitude of the force and the distance ( 378 N)( 84 m) = 31750 Joules.
Generalized Response: q$ = q$ + " When a charge Q, in Coulombs, experiences an electric field E, in N/C, it experiences a force q$ = q$ + " F = Q * E Newtons in or opposite to the direction of the field, depending on whether the q$ = q$ + " product Q * E is positive or negative. If the charge moves a distance `ds, then the work done q$ = q$ + " by this field force on the charge is
W(field on charge) = F `ds q$ = q$ + " = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0q||value missing for q|| When a charge Q, in Coulombs, experiences an electric field E, in N/C, it experiences a force q$ = q$ + " F = Q * E Newtons in or opposite to the direction of the field, depending on whether the q$ = q$ + " product Q * E is positive or negative. If the charge moves a distance `ds, then the work done q$ = q$ + " by this field force on the charge is
W(field on charge) = F `ds q$ = q$ + " = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 When a charge Q, in Coulombs, experiences an electric field E, in N/C, it experiences a force q||value missing for q|| F = Q * E Newtons in or opposite to the direction of the field, depending on whether the q$ = q$ + " product Q * E is positive or negative. If the charge moves a distance `ds, then the work done q$ = q$ + " by this field force on the charge is
W(field on charge) = F `ds q$ = q$ + " = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 F = Q * E Newtons in or opposite to the direction of the field, depending on whether the q||value missing for q|| product Q * E is positive or negative. If the charge moves a distance `ds, then the work done q$ = q$ + " by this field force on the charge is
W(field on charge) = F `ds q$ = q$ + " = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 product Q * E is positive or negative. If the charge moves a distance `ds, then the work done q||value missing for q|| by this field force on the charge is
W(field on charge) = F `ds q$ = q$ + " = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 by this field force on the charge is
W(field on charge) = F `ds q||value missing for q|| = Q * E * `ds.
The work q$ = q$ + " required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 = Q * E * `ds.
The work q||value missing for q|| required to move the charge is equal in magnitude but of opposite sign to the work done on q$ = q$ + " the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 required to move the charge is equal in magnitude but of opposite sign to the work done on q||value missing for q|| the charge by the field. So the work required to move the charge is q$ = q$ + "
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0 the charge by the field. So the work required to move the charge is q||value missing for q||
W(opposed to field) = q$ = q$ + " - W(field on charge) = - Q * E * `ds. 0
W(opposed to field) = q||value missing for q|| - W(field on charge) = - Q * E * `ds.
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Explanation in terms of Figure(s), Extension
Figure description: The figure below shows a straight path of length `ds from a starting point to an ending point, with the path parallel to an electric field . If a charge Q travels from start to finish, it experiences a force F = Q * E in its direction of motion. Thus the work done on the charge is
W(field on charge) = F `ds = Q * E * `ds.
The charge does work to oppose the action of the field, so
W(charge on field) = -W(field on charge) = - Q * E * `ds.
