Phy102&08-II-ms1 - 1 The uniform electric field...

1. The uniform electric field between two conducting charged plates shown in the figure has
a magnitude of E = 28.40 N/C. The plate separation is 1 m, and we launch an electron from
the bottom plate directly upward with v
o
= 3 × 10
6
m/s. Will the electron reach the top plate?
Justify your answer by providing numerical data.
* 2 12
31
19
/ 10 0 . 5
10 11 . 9
40 . 28 10 6 . 1
s m
m
qE
a
y
y
× - =
×
× × -
= =
-
-
*
( )
ο ο
ν ν y y a
y y y
- = - 2 2 2
m H H 90 . 0 10 0 . 5 2 10 9 0 12 12 = → × × - = × -
* Since H < 1m, the electron does not reach to the top plate.
2. Three point charges, 1 μ C each, are placed on three corners of an equilateral triangle with side
a = 1 m. Write the net electric field at the middle point P, in terms of unit vectors.
2 2 2 2
75 . 0 4 m a a r = - =
* C N k
r
q
k E 12
2
3
= =
and
3 3 1 1 3 2 1
E E E E E E E E
r r r r r r r r
= + - = + + =
* C N k E E
x x
4 . 10 30 cos 12
3
= × = =
* C N k E E
y y
0 . 6 30 sin 12
3
= × = =
*
( ) ( )
j C N k i C N k E
ˆ
0 . 6
ˆ
4 . 10 + =
r
y
P
a
x
y
v
o
E
y
x a
r
E
1
E
2
E
3

3. A long non-conducting cylinder with radius a = 0.5 m has a
volume charge density ρ = -5 nC/m
3
. Find the magnitude of electric
field (in N/C) at a distance r = 0.2 m from its axis.
ο
ε
enc
q
dA E = ⋅
∫
r
∫
- = rLE dA E π 2
r
LP r q
enc
2 π =
C N E r E 5 . 56
10 85 . 8 2
2 . 0 10 5
2 12
9
= →
× ×
× × -
- = - =
-
-
ο
ε
ρ
4. A very long line of charge having a uniform charge density λ is at a distance of d = 0.4 m from
a positive point charge (Q = 4 μ C) as shown in the figure. If the net electric field at point A is
zero, find the value of λ (sign and magnitude).