Relation between Electric Potential and Electric Field

AI Thread Summary
The electric field along the x-axis is defined as E = 1.2x - 3.06 N/C. To find the electric potential at (7.22 m, 0) with the potential set to zero at (4.39 m, 0), the potential difference is calculated using the integral of the electric field. The correct calculation yields a potential difference of Vba = -11.054 V, leading to Vb = -11.054 V when Va = 0. This approach clarifies the relationship between electric potential and electric field in the specified region.
Alan I
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Homework Statement


In a certain region of space, the electric field along the x-axis is given by:

E = 1.2x - 3.06, where E is in N/C and x is in meters.

If you set the electric potential equal to zero at (4.39 m,0), find the electric potential, in V, at the point (7.22 m,0).

Homework Equations


V = - ∫E * dl

The Attempt at a Solution


[/B]
V = - ∫ (1.2X-3.06) dx

⇒ V = - [1.2X2/2 - 3.06X]02.83

⇒V=3.85 → which is http://www.dabur.com/odomos/images/wrong_sign.jpg :oldfrown: ...any suggestions?
 
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You have the wrong integration boundaries and you are missing the term due to the potential at x = 4.39 m.
 
Alan I said:

Homework Statement


In a certain region of space, the electric field along the x-axis is given by:
E = 1.2x - 3.06, where E is in N/C and x is in meters.
If you set the electric potential equal to zero at (4.39 m,0), find the electric potential, in V, at the point (7.22 m,0).
First, find the potential difference between the two points.
Then set the one to zero & get the other.
 
rude man said:
First, find the potential difference between the two points.
Then set the one to zero & get the other.

potential difference between the two points: Vba = - ∫4.397.22 (1.2X-3.06) dx

⇒ Vba = -[1.2X2/2-3.06X]4.397.22
= -(9.184+1.870)
= -11.054
⇒-11.054 = Vb - Va

Va=0

⇒Vb = -11.054 V

does that make more sense? :olduhh:
 
Alan I said:
potential difference between the two points: Vba = - ∫4.397.22 (1.2X-3.06) dx

⇒ Vba = -[1.2X2/2-3.06X]4.397.22
= -(9.184+1.870)
= -11.054
⇒-11.054 = Vb - Va

Va=0

⇒Vb = -11.054 V

does that make more sense? :olduhh:
A whole lot more! :smile:

P.S. I didn't check the math.
 
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