Name: Continuous Charge Distribution
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: This video will help us understand the necessity of continuous charge distribution and learn about the concept of linear charge density. Learn more.

Question

The figure $(a)$ and $(b)$ show the field lines of a positive and negative point charge, respectively.

Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$ ; $A$ and $B$ .

Accepted Answer

Case $(b)$ : $U_{Q} - U_{P}$

As we know that potential at a point is potential energy per unit charge.

$B$ where $q$ is the test charge which is taken as a negative charge.

So let $q = - q_{o}$

or $V_{Q} - V_{P} = \frac{U_{Q} - U_{P}}{- q_{o}}$

or $U_{Q} - U_{P} = - q_{o} \times (V_{Q} - V_{P}) . . . (i)$

As we know that electric field flows from higher potential to lower potential, $V_{P} > V_{Q}$ .

Thus, $V_{Q} - V_{P} < 0 . . . (ii)$

Using equations $(i)$ and $(a)$ , we get, $(b)$ , i.e., it is positive.

Case $(b)$ : $U_{A} - U_{B}$

As we know that potential at a point is potential energy per unit charge.

$∆ V = \frac{∆ U}{q}$ where $q$ is the test charge which is taken as a negative charge.

So let $q = - q_{o}$

or $V_{A} - V_{B} = \frac{U_{A} - U_{B}}{- q_{o}}$

or $U_{A} - U_{B} = - q_{o} \times (V_{A} - V_{B}) . . . (i)$

As we know that electric field flows from higher potential to lower potential, $V_{B} > V_{A}$ .

Thus, $V_{A} - V_{B} < 0 . . . (ii)$

Using equations $(i)$ and $(ii)$ , we get, $U_{A} - U_{B} > 0$ , i.e., it is positive.

The figure $(a)$ and $(b)$ show the field lines of a positive and negative point charge, respectively.

Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$ ; $A$ and $B$ .

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

The figure a and b show the field lines of a positive and negative point charge, respectively. Give the sign of the potential energy difference of a small negative charge between the points Q and P; A and B.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

The figure $(a)$ and $(b)$ show the field lines of a positive and negative point charge, respectively.

Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$ ; $A$ and $B$ .