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# Uniform electric field

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A uniform electric field produces an acceleration (10 m/s^2, 10 m/s^2,0) at (1 m, 1m, 1m) for a -5 micro Coloumb charge of mass 10 g. Write the electric field at all points in space. (Hint: it would be a good idea to know what uniform means here).

https://brainmass.com/physics/electric-power/uniform-electric-field-23891

## SOLUTION This solution is FREE courtesy of BrainMass!

(* denotes multiplication, ^ denotes power)
uniform means constant
acceleration comes from the force the electric field applies on the charge as
force = mass * acceleration

Electric force= E*q
where E= Electric field
q=charge
when we equate it to mass * acceleration we get Electric field E as we know the mass and the charge
E=mass*acceleration/charge

We will calculate the three components of the Electric field in x,y and z directions as field is a vector quantity

q= 5 Mu C = 0.000005 C
mass= 10 g = 0.01 Kg

In the x direction
acceleration= ax
ax= 10 m/s^2
mass= 0.01 Kg
Therefore force=mass * acceleration= 0.1 N =0.01*10

Electric field in the x direction= Ex ( to be determined)
q= 0.000005 C
Ex* q= 0.1 N
Therefore
Ex= 20000 V/m =0.1/0.000005

In the y direction
acceleration= ay
ay= 10 m/s^2
mass= 0.01 Kg
Therefore force=mass * acceleration= 0.1 N =0.01*10

Electric field in the y direction= Ey ( to be determined)
q= 0.000005 C
Ey* q= 0.1 N
Therefore
Ey= 20000 V/m =0.1/0.000005

In the z direction
acceleration= az
az= 0 m/s^2
mass= 0.01 Kg
Therefore force=mass * acceleration= 0 N =0.01*0

Electric field in the z direction= Ez ( to be determined)
q= 0.000005 C
Ez* q= 0 N
Therefore
Ez= 0 V/m =0/0.000005

Thus the components of the electric field in the x,y and z directions are

Ex= 20,000 V/m
Ey= 20,000 V/m
Ez= 0

Thus the Electric field is in the xy plane ( as z component is zero)
Magnitude of the Electric field=square root of (Ex^2+ Ey^2)= 28,284 V/m

Its direction is given by
tan theta = Ey/Ex=20000/20000= 1

or theta = 45 degrees

Thus the Electric field makes an angle of 45 degrees with the x axis

Answer: Electric field is 28,284 V/m making an angle of 45 degrees with the x axis

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!