# If the electron is freed up, what would be its acceleration?

## Homework Statement

The Electric Potential on an XY plane is described by the relationship V=2x^2-2y^2. Consider ONLY values in the range [0, 5].

A) Depict on an XY plane three lines of equal potential V=-4V, 0V and 4V. Consider 5 ponts. X= 0, 1, 2, 3, 4, 5.
B) Consider one point where x= 3m, and y= 3m. Estimate the electric field magnitude in volts per meter.
C) For the same point, estimate the direction of the electric field, counting counter-clockwise from the X-axis. If an electron is placed at this point, D) what would be the direction and E) the magnitude of the force acting on it.
F) If the electron is freed up, what would be its acceleration?

## The Attempt at a Solution

A) Don't need help with this.

B) For this question, I am assuming we wouldn't differentiate the the equation given since it is in terms of x and y. Would it be logical to use E=V/x where V is the potential difference between the two closest contours and x is the distance between them passing through (3, 3)?

C) For this question, I am also assuming this is merely conceptual and that there is no calculations to determine the angle. I was going to estimate 120 deg- 135 deg from the +x axis.

D) Wouldn't the electric field from an electron be insignificant relative to this field, therefore the electric field would remain in the direction it was?

E/F) Don't require help.

Thanks!

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G01
Homework Helper
Gold Member

## Homework Statement

The Electric Potential on an XY plane is described by the relationship V=2x^2-2y^2. Consider ONLY values in the range [0, 5].

A) Depict on an XY plane three lines of equal potential V=-4V, 0V and 4V. Consider 5 ponts. X= 0, 1, 2, 3, 4, 5.
B) Consider one point where x= 3m, and y= 3m. Estimate the electric field magnitude in volts per meter.
C) For the same point, estimate the direction of the electric field, counting counter-clockwise from the X-axis. If an electron is placed at this point, D) what would be the direction and E) the magnitude of the force acting on it.
F) If the electron is freed up, what would be its acceleration?

## The Attempt at a Solution

A) Don't need help with this.

B) For this question, I am assuming we wouldn't differentiate the the equation given since it is in terms of x and y. Would it be logical to use E=V/x where V is the potential difference between the two closest contours and x is the distance between them passing through (3, 3)?

C) For this question, I am also assuming this is merely conceptual and that there is no calculations to determine the angle. I was going to estimate 120 deg- 135 deg from the +x axis.

D) Wouldn't the electric field from an electron be insignificant relative to this field, therefore the electric field would remain in the direction it was?

E/F) Don't require help.

Thanks!
B)Remember the more general relation between the electric field and the potential. The x component of the electric field is given by the derivative of V with respect to x:

$$E_x=\frac{dV}{dx}$$

Similarly,

$$E_y=\frac{dV}{dy}$$

C)Once you have the components of the E field vector, finding the direction should be straightforward.

D) You can check easily enough. Workout the value of the electric field from an electron, say, 1m away from the electron. In magnitude, is it much smaller or much bigger or same as the average field given by the above potential. (just roughly estimate)

Could you explain A? I have a similar question and I don't understand it. thanks

Thanks for the response. However, I have a bit of confusion.

Would Ex=d(2x^2)/dx = 4x

and Ey=d(-2y^2)=-4y

When doing this I get E= {12i - 12j} which doesnt really make sense. Help?

Also, for A what you have to do is set the equation equal to y. Then, plug in -4 V, and all of the x points to find the y points that go with it. You will do this for -4, 0, and 4V. Then plot the equipotential curves.

Nevermind. I figured it out.

I have the same question and am having trouble with C) to F)

G01
Homework Helper
Gold Member
Nevermind. I figured it out.
Great!

I have the same question and am having trouble with C) to F)
Can you post your attempt at the solution?

Also, please post part E (the OP never mentioned what the question in part E was.)