Electric field between 2 objects and electric force on object?

[megabassdude]

Homework Statement

Suppose two metal plates are separated by 1.00 cm. These plates are wide:
at least 0.5 m square. We hook wires from a battery to each plate, so that there is a
potential of 500 volts between them.

Homework Equations

(A) Find the electric field between the plates, in
the middle where the field is quite uniform.

(B) Suppose we introduce a small object
which has +2.0 nC (nanocoulombs) of charge on it, placing it between the plates, near
the middle where you just found the electric field. Determine the electric force on this
object.

The Attempt at a Solution

(A)

I'm guessing I use the formula V_AB = Ed.

Step 1

1.00 cm converted to meters = 0.01

Step 2

V_AB = Ed.
500=(E)(0.01).

E = 5.0 x 10⁴ V/m.

Does the width of the plate have any influence though?

(B)

I can't figure out how to do part (B)

I'm thinking I use the formula F = qE.

Step 1

+2.0 nanoCoulomb's converted to Coulombs = +2.0 x 10^-9 C

Step 2

F = qE.
F =(2.0 x 10^-9 C)(5.0 x 10⁴ V/m)
F = 1.0 x 10^-4 N

Again does width of the plate have any influence?

 

[ehild]

Homework Statement

Suppose two metal plates are separated by 1.00 cm. These plates are wide:
at least 0.5 m square. We hook wires from a battery to each plate, so that there is a potential of 500 volts between them.

Homework Equations

(A) Find the electric field between the plates, in the middle where the field is quite uniform.
Again does width of the plate have any influence?

Welcome to PF!

The electric field is uniform far from the edges of the plates, where the electric field lines are uneven and curved. In this problem, the plates are wide so the area near the edges is small compared to the total. The edge effect does not influence the surface charge density far from the edges, consequently, neither the electric field in the middle.

ehild

 

[Simon Bridge]

Looks good to me - though the force and the electric field are both vectors and you have only given magnitudes. For completeness, you should say something about direction.

The setup describes a parallel plate capacitor - the width of the plates does affect the physics but not the bit you need: that is already accounted for in the electric field. The only effect is that the field is not uniform near the edge.

Note: +1nC charge in a 5V/m field experiences a 5nN force :)