A point charge q of mass m is suspended verti | vedclass

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

Question

(C) The initial potential energy of the system is $U_i = 0$.The final potential energy of the system is $U_f = \frac{k q p}{(2l \sin(\alpha/2))^2} + m

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) The initial potential energy of the system is $U_i = 0$.The final potential energy of the system is $U_f = \frac{k q p}{(2l \sin(\alpha/2))^2} + mgh$,where $k = \frac{1}{4\pi\epsilon_0}$.From the geometry of the triangle,the distance $r = 2l \sin(\alpha/2)$.For the charge $q$ in equilibrium,the forces acting are tension $T$,gravity $mg$,and the electric force $F_e = qE$. The electric field of a dipole at distance $r$ is $E = \frac{kp}{r^3} \sqrt{1 + 3\cos^2\phi}$. Given the geometry,the force $F_e = \frac{kqp}{r^3} 	imes 2$ (for the specific orientation).Using the Lami's theorem or the sine rule for equilibrium:$\frac{mg}{\sin(90^\circ + \alpha/2)} = \frac{qE}{\sin(180^\circ - 2	heta)}$.Solving the equilibrium condition leads to $F_e = mg \cdot 2 \sin(\alpha/2)$.Substituting $F_e = \frac{kqp}{r^2} \cdot \frac{2}{r} = \frac{2kqp}{r^3}$,we find that the potential energy $U_f = \frac{kqp}{r^2} + mgh = mgh + mgh = 2mgh$.Since $W = \Delta U = U_f - U_i = 2mgh - 0 = 2mgh$,we have $N = 2$.

Similar Questions

The electric field at a point due to an electric dipole,on an axis inclined at an angle $\theta$ $(< 90^{\circ})$ to the dipole axis,is perpendicular to the dipole axis,if the angle $\theta$ is

An electric dipole with dipole moment $2 \times 10^{-10} \text{ C m}$ is aligned at an angle $30^{\circ}$ with the direction of a uniform electric field of $10^4 \text{ N C}^{-1}$. The magnitude of the torque acting on the dipole is:

The net electric field at the given point $O$ due to all the four identical short electric dipoles of dipole moment $p$ each,as shown in the figure,is $\left( k = \frac{1}{4\pi \varepsilon_0} \right)$.

$A$ dipole is placed in a uniform electric field,its potential energy will be minimum when the angle between its axis and field is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module