A ve ry large metal sh eet has charge moving over it. Th e sheet has a surface c

Question

A ve

ry large metal sh

eet has charge moving

over it. Th

e sheet

has a surface charge density of

?

= 5x10

-

6

C/m

2

.

The charges on the sheet are moving at an average speed of v

s

= 0.0001 m/s.

A proton is located a distance D = 10 cm from the

sheet. The pro

ton i

s headed straight at the sheet with

a speed of v

e

= 1000

0

m/s

What is electric field above the sheet at the point the proton is at
(magnitude and direction)
?
b)
What is the surface current
density of the sheet?
c)
What is the magnetic field above the sheet at the point the proton is at
(magnitude and
direction)
?
d)
What is the electro
-
static force on the proton
(
magnitude and direction
)
?
e)
What is the
magnetic force on the proton
(magnitude and direction)
?
f)
How does the elect
ro
-
static force compare to the magnetic force (which is bigger and by how
many times
bigger is it
)?
g)
Approximately
how close will the proton get to the plate?
(is there a force you can neglect?)

Explanation / Answer

apply electrical force = gravitational force

ma = Eq

E = ma/q

also Electric field E = sigma/2eo

E = 5 e-6 /(2* 8.85 e-12 )

E = 2.82 *10^5 N/C

-----------------------------------------

apply accleration a = v^2-u^2/2S

a = 1000^2 - 0.0001^2/(2* 0.1)

a = 5 e6 m/s^2

so

E = 1.67 e -27 * 5 e 6/(1.6 e-19)

E = 5.21 e -2 N/C

-------------------------------

as Electric field and magnetic field are related by E = Bv

so

magnetic field B = E/v

B = 5.21 e -2/1000

B = 52 uT

-------------------------------

magnetic fiorce F = qvB

F = 1.6 e-19 * 1000 * 52 e-6

F = 5.21 e-5 N

------------------------

apply r = mv/qB

r = 1.67 e-27 * 1000/(1.6 e-19 * 52 e-6)

f = 0.2 m

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