A small bob of mass 100 mg and charge +10 m | vedclass

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

Question

(D) At equilibrium,the forces acting on the bob are the tension $T$ in the string,the gravitational force $mg$ acting downwards,and the electric force

Vedclass · Accepted Answer

$1.77$

Vedclass · Answer

(D) At equilibrium,the forces acting on the bob are the tension $T$ in the string,the gravitational force $mg$ acting downwards,and the electric force $F_e = qE$ acting horizontally away from the sheet.For an infinitely long nonconducting sheet,the electric field is $E = \frac{\sigma}{2\varepsilon_0}$.Resolving the forces at equilibrium:$T \sin(45^{\circ}) = F_e = qE = q \left( \frac{\sigma}{2\varepsilon_0} ight)$$T \cos(45^{\circ}) = mg$Dividing the two equations:$	an(45^{\circ}) = \frac{q\sigma}{2\varepsilon_0 mg}$Since $	an(45^{\circ}) = 1$,we have:$1 = \frac{q\sigma}{2\varepsilon_0 mg} \implies \sigma = \frac{2\varepsilon_0 mg}{q}$Given values: $m = 100 \ mg = 100 	imes 10^{-6} \ kg = 10^{-4} \ kg$,$q = 10 \ \mu C = 10^{-5} \ C$,$g = 10 \ m/s^2$,$\varepsilon_0 = 8.85 	imes 10^{-12} \ F/m$.Substituting the values:$\sigma = \frac{2 	imes 8.85 	imes 10^{-12} 	imes 10^{-4} 	imes 10}{10^{-5}}$$\sigma = 17.7 	imes 10^{-12} 	imes 10^2 = 17.7 	imes 10^{-10} \ C/m^2 = 1.77 	imes 10^{-9} \ C/m^2 = 1.77 \ nC/m^2$.

Similar Questions

$A$ charge $q$ is placed at one corner of a cube. The electric flux through any of the three faces adjacent to the charge is zero. The flux through any one of the other three faces is

The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2 \text{ V}$. The electric charge enclosed in a cube of $1 \text{ m}$ side with its centre at the origin is (in coulomb):

$A$ thin disc of radius $b = 2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $\sigma$. If the electric field on its axis at height $h$ $(h << a)$ from its centre is given as $Ch$,then the value of $C$ is:

$A$ particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as (Consider $k$ as Coulomb's constant).

Vedclass Test Series

Exam Paper Generator

Online Exam Module