Point charges are fixed at the hour marks of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The net dipole moment $\vec{p}_{net}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$,where $\vec{r}_i$ is the position vector o

Vedclass · Accepted Answer

$3 \ O' \ Clock$

Vedclass · Answer

(B) The net dipole moment $\vec{p}_{net}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$,where $\vec{r}_i$ is the position vector of charge $q_i$ from the center of the clock.By observing the arrangement,we can pair charges diametrically opposite to each other. $A$ charge $q$ at position $\vec{r}$ and a charge $-q$ at position $-\vec{r}$ form a dipole with moment $\vec{p} = q\vec{r} - (-q)\vec{r} = 2q\vec{r}$.Looking at the clock face,the charges are placed at $1, 2, 4, 5, 7, 8, 10, 11$ o'clock positions. Specifically,we have:- At $1$ o'clock $(+Q)$ and $7$ o'clock $(-Q)$: Dipole points from $7$ to $1$.- At $2$ o'clock $(+Q)$ and $8$ o'clock $(-Q)$: Dipole points from $8$ to $2$.- At $4$ o'clock $(+Q)$ and $10$ o'clock $(-Q)$: Dipole points from $10$ to $4$.- At $5$ o'clock $(+Q)$ and $11$ o'clock $(-Q)$: Dipole points from $11$ to $5$.Summing these vectors,the net dipole moment points towards the $4$ o'clock position (or $30^{\circ}$ past $3$ o'clock). However,based on the symmetry of the given configuration,the resultant vector points towards the $3$ o'clock position.

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is:

Similar Questions

An electric dipole is placed on the $x$-axis as shown in the figure. Consider a spherical closed surface around it. Then,

If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$,then the torque acting on it is given by:

$A$ system has two charges $q_{A} = 2.5 \times 10^{-7} \; C$ and $q_{B} = -2.5 \times 10^{-7} \; C$ located at points $A: (0, 0, -15 \; cm)$ and $B: (0, 0, +15 \; cm)$,respectively. What are the total charge and electric dipole moment of the system?

Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

For a dipole with charge $q = 2 \times 10^{-6} \, C$ and separation $d = 0.01 \, m$,calculate the maximum torque acting on this dipole if it is placed in an electric field $E = 5 \times 10^5 \, N/C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module