An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E = - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cyllnder?
An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E = - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cyllnder?
$(a)$ We can see from the figure that on the left face $E$ and $\Delta S$ are parallel. Therefore, the outward flux is
$\phi_{L}= E \cdot \Delta S =-200 \hat{ i } \cdot \Delta S$
$=+200 \Delta S, \text { since } \hat{ i } \cdot \Delta S =-\Delta S$
$=+200 \times \pi(0.05)^{2}=+1.57 \,N\, m ^{2} \,C ^{-1}$
On the right face, $E$ and $\Delta S$ are parallel and therefore
$\phi_{R}= E \cdot \Delta S =+1.57 \,N\,m ^{2} \,C ^{-1}$
$(b)$ For any point on the side of the cylinder $E$ is perpendicular to $\Delta s$ and hence $E \cdot \Delta S =0 .$ Therefore, the flux out of the side of the cylinder is zero.
$(c)$ Net outward flux through the cylinder
$\phi=1.57+1.57+0=3.14 \,N\, m ^{2} \,C ^{-1}$
$(d)$ The net charge within the cylinder can be found by using Gauss's law which gives
$q=\varepsilon_{0} \phi$
$=3.14 \times 8.854 \times 10^{-12}\, C$
$=2.78 \times 10^{-11}\, C$
Similar Questions
Figure shows the electric field lines around three point charges $A, \,B$ and $C$.
$(a)$ Which charges are positive ?
$(b)$ Which charge has the largest magnitude ? Why ?
$(c)$ In which region or regions of the picture could the electric field be zero ? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere
Figure shows the electric field lines around three point charges $A, \,B$ and $C$.
$(a)$ Which charges are positive ?
$(b)$ Which charge has the largest magnitude ? Why ?
$(c)$ In which region or regions of the picture could the electric field be zero ? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere
The electric flux passing through the cube for the given arrangement of charges placed at the corners of the cube (as shown in the figure) is
The electric flux passing through the cube for the given arrangement of charges placed at the corners of the cube (as shown in the figure) is
Three positive charges of equal value $q$ are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in
Three positive charges of equal value $q$ are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in
- [AIEEE 2012]
A charge $'q'$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow{ E }$ through the shaded area is ...... .
A charge $'q'$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow{ E }$ through the shaded area is ...... .
- [JEE MAIN 2021]
A metallic shell has a point charge ‘$q$’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces
A metallic shell has a point charge ‘$q$’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces
- [IIT 2003]