Which of the following statement$(s)$ is/are correct?
$(A)$ If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$,then the Gauss law will still be valid.
$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.
$(C)$ If the electric field between two point charges is zero somewhere,then the sign of the two charges is the same.
$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $(V_B - V_A)$.
$(A)$ If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$,then the Gauss law will still be valid.
$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.
$(C)$ If the electric field between two point charges is zero somewhere,then the sign of the two charges is the same.
$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $(V_B - V_A)$.
- A$(A, B)$
- B$(C, D)$
- C$(A, D)$
- D$(B, C)$
Explore More
Similar Questions
Two charged particles,each of mass $3 \ g$ and charge $0.2 \ \mu C$,stay in (vacuum) equilibrium on a horizontal surface with a separation of $20 \ cm$. The coefficient of friction is $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}\right]$ and $\left(g=10 \ ms^{-2}\right)$.
The electric field $E$ is measured at a point $P(0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions,along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.
List-$I$ List-$II$ $P$. $E$ is independent of $d$ $1$. $A$ point charge $Q$ at the origin $Q$. $E \propto \frac{1}{d}$ $2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$. $R$. $E \propto \frac{1}{d^2}$ $3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$ $S$. $E \propto \frac{1}{d^3}$ $4$. Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along $(y=0, z=l)$ has a charge density $+\lambda$ and the one along $(y=0, z=-l)$ has a charge density $-\lambda$. Take $2l \ll d$ $5$. Infinite plane with uniform surface charge density
| List-$I$ | List-$II$ |
|---|---|
| $P$. $E$ is independent of $d$ | $1$. $A$ point charge $Q$ at the origin |
| $Q$. $E \propto \frac{1}{d}$ | $2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$. |
| $R$. $E \propto \frac{1}{d^2}$ | $3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$ |
| $S$. $E \propto \frac{1}{d^3}$ | $4$. Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along $(y=0, z=l)$ has a charge density $+\lambda$ and the one along $(y=0, z=-l)$ has a charge density $-\lambda$. Take $2l \ll d$ |
| $5$. Infinite plane with uniform surface charge density |
The diagrams depict four different charge distributions. All the charged particles are at the same distance $r$ from the origin $(i.e., OA = OB = OC = OD = r)$. $F_1, F_2, F_3,$ and $F_4$ are the magnitudes of the electrostatic force experienced by a point charge $q_0$ kept at the origin in Figure-$1$,Figure-$2$,Figure-$3$,and Figure-$4$ respectively. Choose the correct statement.
Medium
View SolutionAn oil drop carries six electronic charges,has a mass of $1.6 \times 10^{-12} \text{ g}$ and falls with a terminal velocity in air. The magnitude of the vertical electric field required to make the drop move upward with the same speed as it was formerly moving is ........$kN/C$.
Medium
View Solution$A$ negatively charged plate has a surface charge density of $2 \times 10^{-6} \, C/m^2$. Find the minimum initial distance of an electron moving toward the plate such that it does not strike the plate,given that its initial kinetic energy is $200 \, eV$.
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo