Q 21 :

As shown in the figure, a configuration of two equal point charges ($q_0=+2\mu \text{C}$) is placed on an inclined plane. The mass of each point charge is 20 g. Assume that there is no friction between the charge and the plane. For the system of two point charges to be in equilibrium (at rest), the height $h=x\times {10}^{-3}\text{ m}.$ The value of $x$ is ______. 

(Take $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{ N m}}^2{\text{C}}^{-2},$$g=10{\text{ ms}}^{-1}$)               [2023]

Q 22 :

Six point charges are kept $60°$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______.

(${\epsilon }_0$ is permittivity of free space)           [2026]

• $-\left(\frac{5Q}{8\pi {\epsilon }_0{R}^2}\right)(\hat{i}-3\hat{j})$

   

• $\frac{Q}{4\pi {\epsilon }_0{R}^2}(\sqrt{3}\hat{i}-\hat{j})$

   

• $-\frac{5Q}{8\pi {\epsilon }_0{R}^2}(\hat{i}+\sqrt{3}\hat{j})$

   

• $-\frac{Q}{4\pi {\epsilon }_0{R}^2}(\sqrt{3}\hat{i}-\hat{j})$

   

Q 23 :

A simple pendulum has a bob with mass $m$ and charge $q$. The pendulum string has negligible mass. When a uniform and horizontal electric field $\overrightarrow{E}$ is applied, the tension in the string changes. The final tension in the string, when the pendulum attains an equilibrium position, is _______. 

(g = acceleration due to gravity)                  [2026]

• $mg\mathit{-}qE$

   

• $mg\mathit{+}qE$

   

• $\sqrt{m^2{g}^2-q^2{E}^2}$

   

• $\sqrt{m^2{g}^2+q^2{E}^2}$

   

Q 24 :

If $\epsilon ,E$ and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :       [2026]

• Am

   

• $A/m²$

   

• A/m

   

• $A·m²$