Q 11 :

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is

• $\frac{2\lambda }{{\epsilon }_0}$

   

• $\frac{\lambda }{2{\epsilon }_0}$

   

• $\frac{\lambda }{4{\epsilon }_0}$

   

• $\frac{\lambda }{{\epsilon }_0}$

   

Q 12 :

Figure shows part of a circuit. What is the potential difference $V_C-V_B=$ __________  $V$

Q 13 :

Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\frac{E_{S_1}}{E_{S_2}}$ is _______.               [2026]

• $\frac{3}{2}$

   

• $\frac{2}{3}$

   

• $\frac{4}{9}$

   

• $\frac{9}{4}$

   

Q 14 :

Two metal plates (A, B) are kept horizontally with separation of $\left(\frac{12}{\pi }\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 ${\text{g/cm}}^3$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are _______.

(Neglect the air resistance to the droplets and take $g=10{\text{m/s}}^2$)                  [2026]

• 100 V and 580 V

   

• 580 V and 100 V

   

• 60 V and 400 V

   

• 0 V and −200 V

   

Q 15 :

The electric potential as a function of $x,y$ is given by $V=5(x^2-y^2)V.$ The electric field at a point (2, 3) m is _____ V/m.             [2026]

• $(-20\hat{i}+30\hat{j})$

   

• $(20\hat{i}-30\hat{j})$

   

• $(20\hat{i}+45\hat{j})$

   

• $(-4\hat{i}+6\hat{j})$