Physics equations/19-Electric Potential and Electric Field/Q:UsingGaussLaw
Equations for this quiz
Solutions (pdf)
testbank
A
1
A cylinder of radius, R, and height H has a uniform charge density of
ρ
{\displaystyle \rho }
. The height is much less than the radius:
H << R
. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
ε
0
E
=
ρ
z
{\displaystyle \varepsilon _{0}E=\rho z}
b)
ε
0
E
=
H
ρ
{\displaystyle \varepsilon _{0}E=H\rho }
c)
ε
0
E
=
H
ρ
z
{\displaystyle \varepsilon _{0}E=H\rho z}
d) none of these are correct
e)
ε
0
E
=
H
ρ
/
2
{\displaystyle \varepsilon _{0}E=H\rho /2}
2
A cylinder of radius, R, and height H has a uniform charge density of
ρ
{\displaystyle \rho }
. The height is much less than the radius:
H << R
. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
ε
0
E
=
H
ρ
/
2
{\displaystyle \varepsilon _{0}E=H\rho /2}
b) none of these are correct
c)
ε
0
E
=
ρ
z
{\displaystyle \varepsilon _{0}E=\rho z}
d)
ε
0
E
=
H
ρ
{\displaystyle \varepsilon _{0}E=H\rho }
e)
ε
0
E
=
H
ρ
z
{\displaystyle \varepsilon _{0}E=H\rho z}
3
A sphere has a uniform charge density of
ρ
{\displaystyle \rho }
, and a radius or R. What formula describes the electric field at a distance r > R?
none of these are correct
b)
r
2
ε
0
E
=
R
3
ρ
/
2
{\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}
c)
r
2
ε
0
E
=
r
3
ρ
/
3
{\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}
d)
r
2
ε
0
E
=
r
3
ρ
/
2
{\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}
e)
r
2
ε
0
E
=
R
3
ρ
/
3
{\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}
4
A sphere has a uniform charge density of
ρ
{\displaystyle \rho }
, and a radius equal to R. What formula describes the electric field at a distance r < R?
r
2
ε
0
E
=
r
3
ρ
/
2
{\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}
b)
r
2
ε
0
E
=
R
3
ρ
/
3
{\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}
c) none of these are correct
d)
r
2
ε
0
E
=
r
3
ρ
/
3
{\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}
e)
r
2
ε
0
E
=
R
3
ρ
/
2
{\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}
5
A cylinder of radius, R, and height H has a uniform charge density of
ρ
{\displaystyle \rho }
. The height is much greater than the radius:
H >> R
. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?
2
R
ε
0
E
=
r
2
ρ
{\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }
b)
2
r
ε
0
E
=
R
2
ρ
{\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }
c)
2
ε
0
E
=
r
ρ
{\displaystyle 2\varepsilon _{0}E=r\rho }
d) none of these are correct
e)
2
r
2
ε
0
E
=
R
3
ρ
{\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }
6
A cylinder of radius, R, and height H has a uniform charge density of
ρ
{\displaystyle \rho }
. The height is much greater than the radius:
H >> R
. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?
2
R
ε
0
E
=
r
2
ρ
{\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }
b)
2
ε
0
E
=
r
ρ
{\displaystyle 2\varepsilon _{0}E=r\rho }
c)
2
r
ε
0
E
=
R
2
ρ
{\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }
d) none of these are correct
e)
2
r
2
ε
0
E
=
R
3
ρ
{\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }