The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is
The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is
- A
${E_0}{\varepsilon _0}\frac{{{l^2}}}{2}$
- B
${E_0}{\varepsilon _0}\pi {r^2}{l^2}$
- C
${E_0}{\varepsilon _0}\pi {r^2}l$
- D
$2{E_0}{\varepsilon _0}\pi {r^2}l$
Similar Questions
$(a)$ Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by
$\left( E _{2}- E _{1}\right) \cdot \hat{ n }=\frac{\sigma}{\varepsilon_{0}}$
where $\hat{ n }$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point. (The direction of $\hat { n }$ is from side $1$ to side $2 .$ ) Hence, show that just outside a conductor, the electric field is $\sigma \hat{ n } / \varepsilon_{0}$
$(b)$ Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.
$(a)$ Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by
$\left( E _{2}- E _{1}\right) \cdot \hat{ n }=\frac{\sigma}{\varepsilon_{0}}$
where $\hat{ n }$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point. (The direction of $\hat { n }$ is from side $1$ to side $2 .$ ) Hence, show that just outside a conductor, the electric field is $\sigma \hat{ n } / \varepsilon_{0}$
$(b)$ Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.
Three infinitely long charge sheets are placed as shown in figure. The electric field at point $P$ is
Three infinitely long charge sheets are placed as shown in figure. The electric field at point $P$ is
- [IIT 2005]
A conducting sphere of radius $10\, cm$ has unknown charge. If the electric field at a distance $20\, cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is
A conducting sphere of radius $10\, cm$ has unknown charge. If the electric field at a distance $20\, cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is
The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho$ (r) [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure The electric field is only along rhe radial direction.
Figure:$Image$
$1.$ The electric field at $\mathrm{r}=\mathrm{R}$ is
$(A)$ independent of a
$(B)$ directly proportional to a
$(C)$ directly proportional to $\mathrm{a}^2$
$(D)$ inversely proportional to a
$2.$ For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is
$(A)$ $\frac{3 Z e}{4 \pi R^3}$ $(B)$ $\frac{3 Z e}{\pi R^3}$ $(C)$ $\frac{4 Z e}{3 \pi R^3}$ $(D)$ $\frac{\mathrm{Ze}}{3 \pi \mathrm{R}^3}$
$3.$ The electric field within the nucleus is generally observed to be linearly dependent on $\mathrm{r}$. This implies.
$(A)$ $a=0$ $(B)$ $\mathrm{a}=\frac{\mathrm{R}}{2}$ $(C)$ $a=R$ $(D)$ $a=\frac{2 R}{3}$
Give the answer question $1,2$ and $3.$
The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho$ (r) [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure The electric field is only along rhe radial direction.
Figure:$Image$
$1.$ The electric field at $\mathrm{r}=\mathrm{R}$ is
$(A)$ independent of a
$(B)$ directly proportional to a
$(C)$ directly proportional to $\mathrm{a}^2$
$(D)$ inversely proportional to a
$2.$ For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is
$(A)$ $\frac{3 Z e}{4 \pi R^3}$ $(B)$ $\frac{3 Z e}{\pi R^3}$ $(C)$ $\frac{4 Z e}{3 \pi R^3}$ $(D)$ $\frac{\mathrm{Ze}}{3 \pi \mathrm{R}^3}$
$3.$ The electric field within the nucleus is generally observed to be linearly dependent on $\mathrm{r}$. This implies.
$(A)$ $a=0$ $(B)$ $\mathrm{a}=\frac{\mathrm{R}}{2}$ $(C)$ $a=R$ $(D)$ $a=\frac{2 R}{3}$
Give the answer question $1,2$ and $3.$
- [IIT 2008]
A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to
A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to
- [AIIMS 1997]