The value of potential difference between two points

[Fatima Hasan]

Homework Statement

Homework Equations

##ΔV=Ed##

The Attempt at a Solution

##V_A=E l##
##V_b=0## , because point B is perpendicular to the electric field
##ΔV = V_a + V_b##
= El
Is my answer correct ?

 

[drvrm]

The Attempt at a Solution

VA=ElVA=ElV_A=E l
Vb=0Vb=0V_b=0 , because point B is perpendicular to the electric field , so Eb=0Eb=0E_b=0
ΔV=Va+VbΔV=Va+VbΔV = V_a + V_b
= El
Is my answer correct ?

your answer seems to be correct only in number but the arguments and calculation is to be corrected
follow a method...take a test charge on the path and calculate the work done.
why you are saying that Eb=0?

 

[Fatima Hasan]

why you are saying that Eb=0

##V_b = 0## and ##E_b≠0##

 

[drvrm]

Vb=0Vb=0V_b = 0 and Eb≠0

if electric field is there then potential at a point can not be zero , the potential is zero at infinity.
E(b) can have a value may be same as the tip of the path from where it starts to go perpendicular to the field.
the work done is dot product of force and displacement.

 

[Fatima Hasan]

if electric field is there then potential at a point can not be zero , the potential is zero at infinity.
E(b) can have a value may be same as the tip of the path from where it starts to go perpendicular to the field.
the work done is dot product of force and displacement.

I am asked about the value of the potential difference and since both points have the same electric potential which is ##E l## , so ##V_{ab} = V_b-V_a ##
##= El-El = 0##

 

[Doc Al]

Instead of thinking in terms of Va or Vb, which requires defining a reference point, think in terms of changes in V. If you like, you can call that point where the arrows connect "C".

 

[drvrm]

I am asked about the value of the potential difference and since both points have the same electric potential which is ElElE l , so Vab=Vb−VaVab=Vb−VaV_{ab} = V_b-V_a
=El−El=0

suppose in an electric field you travel a distance l then work done will not be zero.
for example in a gravitational field you raise or lower a mass through height h there exists a potential difference .
similarly when one travels in a electric field the work done will be force into displacement.

 

[Fatima Hasan]

Sounds correct now?

If yes, I would be grateful if someone could solve it with another method (by reference third point) :)

 

[Doc Al]

Sounds correct now?

No. ##\Delta V = \vec{E}\cdot\vec{d} \neq Ed##

If yes, I would be grateful if someone could solve it with another method (by reference third point) :)

I thought that's what you attempted in your first post. Try again, more carefully. (You almost had it right.) Call the third point X. Vab = Vax + Vxb.

 

[Fatima Hasan]

Call the third point X. Vab = Vax + Vxb.

##V_{ab} = V_a+V_b##
= ##El + El##
##= 2 El##

 

[Doc Al]

##V_{ab} = V_a+V_b##
= ##El + El##
##= 2 El##

No. Just rewrite what you did originally using ##V_{ax}## and ##V_{xb}##. (Instead of ##V_{a}## and ##V_{b}##, which are potentials at a point.)

 

[Fatima Hasan]

No. Just rewrite what you did originally using ##V_{ax}## and ##V_{xb}##. (Instead of ##V_{a}## and ##V_{b}##, which are potentials at a point.)

## \displaystyle V_{ax} = E\cdot l ##
## \displaystyle V_{xb} = 0 ##
## \displaystyle \Delta V_{ab} = V_{ax} + V_{xb} = E\cdot l ##

 

[Doc Al]

## \displaystyle V_{ax} = E\cdot l ##
## \displaystyle V_{xb} = 0 ##
## \displaystyle \Delta V_{ab} = V_{ax} + V_{xb} = E\cdot l ##

Good!

 

[harambe]

## \displaystyle V_{ax} = E\cdot l ##
## \displaystyle V_{xb} = 0 ##
## \displaystyle \Delta V_{ab} = V_{ax} + V_{xb} = E\cdot l ##

This is correct