Electrostatics, electric fields and electric potential

[pyroknife]

THe following is a homework assignment from AP Physics.

Homework Statement

Two large, flat parallel conducting plates are .10m apart. THe lower plate has a Voltage of 10v while the upper plate has a voltage of 20V. Point P is located .04m from the bottom plate.
Find:
a) THe magnitude of the electric potential at point P is? Choices: a.) 10v b.)14V c.)16V d.) 20V E.) 0V
b) the direction of the electric field at point P is? a.)up b. down c. left d. right e. 0
c) The magnitude of the electric field at P. a. 0 v/m b.10 v/m c. 40 v/m d. 100 v/m e. 140 v/m

Homework Equations

E=V/D probably the only one
W=q*change in Voltage
W=work
E=E field
V=voltage
D=distance
q=charge

The Attempt at a Solution

My main question is question a.) and b.) i have an idea for a.) but not sure if it's right. And b.) I just have no idea. Question c.) needs the answer to a.)

I didn't really know how to do a so i just took a guess and picked 14V. Since the plates are .1m apart and Point p is .04m above it I just assumed you add 4 volts to 10 to make it 14.
thanks

 

[JoAuSc]

I don't know how much you're expected to know in AP physics, but I would use Laplace's equation, which in one dimension states that

V''(x) = 0

in regions where there is no charge. (Test charges don't count.) x is the distance from one plate (let's say from the V=10 plate) to the other plate. By integrating the equation twice we see that V(x) must be linear. Plug in the voltage values for each of the two plates to get the slope and intercept values. For part b, you need to know that

E(x) = -V'(x)

The electric field points in the direction where V'(x) decreases.

 

[pyroknife]

hmmm yeah we've never learned that, but my physics teacher is known for putting stuff on tests that we haven't learned before.

 

[borgwal]

You don't need to know the Laplace equation here. In fact, all you need is the equation given by the poster: E=V/d, and realize what is meant is the E-field is constant. That will answer both a and c; for b you only have to think about whether the E-field points from positive to negative potential or the other way around.