Determine electric field at x=1m

In summary, the electric potential in a given region is V=ax^2+bx+c, with specific values for a, b, and c. To determine the electric field at x=1m, the derivative of V is needed. The position where the electric field is zero cannot be determined without further information. The equation V=k\frac{Q}{r} does not apply in this situation and there is a negative sign involved in the relationship between electric potential and electric field.
  • #1
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Homework Statement


A. The electric potential in a certain region is
[tex]V=ax^2+bx+c[/tex]
where [itex]a=13\frac{V}{m^2}[/itex], [itex]b=-14\frac{V}{m}[/itex], and [itex]c=50V[/itex].

Determine the electric field at [itex]x=1m[/itex].
Answer in units of [itex]\frac{V}{m}[/itex].

B. Determine the position where the electric field is zero. Answer in units of m.

Homework Equations


[itex]∫Edx=V[/itex]

The Attempt at a Solution


Well V=49. I have no doubt about that. So if V is 49 at x=1, wouldn't the electric field also be 49 at x=1?
 
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  • #2
There is no reason why the electric field should have the same numerical value as the potential.
Note that this comparison has no physical meaning anyway - potential and field have different units.
 
  • #3
[itex]E=\frac{V}{r}[/itex]. [itex]\frac{49}{1}=49[/itex]. What am I doing wrong?
 
  • #4
E=V/r is not right.
E is the derivative of V.
 
  • #5
Oh wow. So [itex]V=k\frac{Q}{r}[/itex] isn't correct?
 
  • #6
Jd0g33 said:
Oh wow. So [itex]V=k\frac{Q}{r}[/itex] isn't correct?

Not for this problem. [itex]V=k\frac{Q}{r}[/itex] only applies for situations involving spherical charge symmetry, like a point charge.
 
  • #7
Oh, and don't forget that there is a negative sign involved in the relationship between electric potential and electric field. The equation that you listed in the "Relevant Equations" section erroneously neglects this.
 
  • #8
Perfect, thank you guys
 

1. What is an electric field?

An electric field is a physical quantity that describes the strength and direction of the force that a charged particle would experience at a given point in space.

2. How is the electric field at a specific point determined?

The electric field at a specific point is determined by calculating the force exerted on a test charge placed at that point by other charged particles in the surrounding space.

3. What is the unit of measurement for electric field?

The unit of measurement for electric field is Newtons per Coulomb (N/C).

4. Why is the electric field at x=1m important?

The electric field at x=1m is important because it allows us to understand the behavior of charged particles in that specific location and how they interact with other charged particles in the surrounding space.

5. How does the electric field at x=1m affect nearby charged particles?

The electric field at x=1m will exert a force on any charged particles in its vicinity, causing them to either be attracted or repelled depending on their own charge. This force can also cause the charged particles to move or accelerate in a certain direction.

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