Question

A charge q is projected into a uniform electric field E, work done when it suffers a displacement Y along the field direction is
$
  A.qEY \\
  B.\dfrac{{qY}}{E} \\
  C.\dfrac{{qE}}{Y} \\
  D.\dfrac{Y}{{qE}} \\
 $

Answer 1

Hint: Electric charge will experience force due to electric field E. Work done is force times the displacement done by the electric charge in the direction of field.

Complete step by step answer:
A charge q generates an electric field around itself in the space. An electric field is the space around the charge where we can experience the force of the charge. It is given by force experienced by a unit charge q. A uniform electric field is the field whose magnitude remains uniform all around the space where its presence can be experienced. So the force experienced due to that electric field E also remains the same.
As electric field and force both are vector quantities meaning having both direction as well as magnitude, therefore the direction of the electric field is the same as of the force applied.
$
  E = \dfrac{F}{q} \\
  \Rightarrow F = Eq \\
 $
From above we can say the force experienced by the charge is electric field E times charge q.
Force is responsible for the change in the motion of anybody here in this case electric charge will experience a change in the motion and that will be happening due to external electric field E. Force and work done are closely related with each other. As work done equals force times distance. Work is also a vector quantity, the direction of work done will be the same as the direction of force applied.
$
  W = F.d \\
  \Rightarrow W = Eqd \\
 $
Given the distance d moved is Y along the field direction
$d = Y$
Putting the values, we get
$W = EqY$
Rearranging the terms, we get
$W = qEY$
This is option A. So the right answer is option A.

Additional Information: When a charge is placed in the uniform electric field it will experience a displacement in the direction of the electric field. That displacement is due to force experienced by the charge in the electric field and Work done is simply force times displacement.

Note:Electric charge will experience a force in the presence of an external electric field. That force will cause the displacement Y. We need to know the terms of the electric field and its relation with force. Force times distance moved in the direction of force is called work. Work done is closely related with force applied on the electric charge to have displacement Y in the direction of the field.