Uniformly charged long cylinder has volume charge density p .Find the electric field at a distance x(

Open in App

Solution

$T h e e l e c t r i c f i e l d d u e t o u n i f o r m l y s p a c e c h a r g e d c y l i n d e r w i t h c h a r g e d e n s i t y ρ a t a d i s \tan c e x i s g i v e n b y; E = \frac{1}{4 π ε_{0}} \times \int_{V} \frac{ρ d V}{x^{2}} W h e n c y l i n d e r i s l o n g t h e o n c o n s t r u c t i n g G a u s s i a n s u r f a c e a t d i \tan c e x, w e g e t; \oint E . d S = \int_{V} \frac{ρ d V}{ε_{0}} o r E \times π r^{2} = \frac{ρ π r^{2} l}{ε_{0}} o r E = \frac{ρ l}{ε_{0}}$

Suggest Corrections

Similar questions

Q. Uniformly charged long cylinder has volume charge density

ρ

. Find the electric field at a distance x < R from the axis of the cylinder.

Q. A long cylinder contains uniformly distributed charge density

ρ

. The electric field at a point

P

inside the cylinder at a distance

x

from the axis is :

A long cylindrical volume contains a uniformly distributed charge of density $ρ$ . Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (figure 30-E5)

Q. A long solid non-conducting cylinder of radius

10 cm

contains a uniformly distributed charge of density

10 {nC/m}^{3}

. Find the magnitude of electric field at a point

P

inside the cylindrical volume at a distance

5 cm

from its axis.
(Take

ϵ_{o} = 9 \times 10^{- 12} C^{2} / {N-m}^{2}

)

Q. A spherical volume has a uniformly distributed charge density

2 \times 10^{- 4} C m^{- 3}

. The electric field at a point inside the volume at a distance 4.0 cm from the centre is :

Join BYJU'S Learning Program

Uniformly charged long cylinder has volume charge density p .Find the electric field at a distance x(

The electric field due to uniformly space charged cylinder with charge density ρat a distance x is given by; E=14πε0×∫VρdVx2When cylinder is long the on constructing Gaussian surface at ditance x, we get; ∮E.dS=∫VρdVε0 or E×πr2=ρπr2lε0or E=ρlε0