1
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1 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 : A
$$\frac{\lambda}{2\in_0}$$
B
$$\frac{\lambda}{\in_0}$$
C
$$\frac{2\lambda}{\in_0}$$
D
$$\frac{\lambda}{4\in_0}$$
2
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 If two charges q$$_1$$ and q$$_2$$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

A
$$d\sqrt k$$
B
$$1\,.\,5d\sqrt k$$
C
$$k\sqrt d$$
D
$$2d\sqrt k$$
3
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other with a force of $$\mathrm{F}$$. Another identical uncharged sphere $$\mathrm{C}$$ is first placed in contact with $$\mathrm{A}$$ and then in contact with $$\mathrm{B}$$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

A
3F/2
B
3F/4
C
F
D
2F
4
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 A spherically symmetric charge distribution is considered with charge density varying as

$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases}$$

Where, $$r(r < R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be: A
$$\frac{\rho_{0} \mathrm{r}}{4 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$$
B
$$\frac{\rho_{0} r}{3 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$$
C
$$\frac{\rho_{0} r}{4 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$$
D
$$\frac{\rho_{0} r}{5 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$$
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