1
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$2 \mathrm{q}$$ are placed on $x$-axis at a distance $$x=0, x=\frac{3}{4} R$$ and $$x=R$$ respectively from origin as shown. If $$\mathrm{q}=2 \times 10^{-6} \mathrm{C}$$ and $$\mathrm{R}=2 \mathrm{~cm}$$, the magnitude of net force experienced by the charge $$-2 q$$ is ___________ N.

2
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1

A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5 \mathrm{~m}$$ distance from each other. Points 'P' and 'Q' are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, respectively. '$$\mathrm{E}_{\mathrm{P}}$$' and '$$\mathrm{E}_{\mathrm{Q}}$$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $$\frac{E_{p}}{E_{0}}=\frac{4}{a}$$ for $$2|\sigma|=|\lambda|$$, then the value of $$a$$ is ___________.

3
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1

64 identical drops each charged upto potential of $$10 ~\mathrm{mV}$$ are combined to form a bigger drop. The potential of the bigger drop will be __________ $$\mathrm{mV}$$.

4
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1

As shown in the figure, a configuration of two equal point charges $$\left(q_{0}=+2 \mu \mathrm{C}\right)$$ is placed on an inclined plane. Mass of each point charge is $$20 \mathrm{~g}$$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $$\mathrm{h}=x \times 10^{-3} \mathrm{~m}$$.

The value of $$x$$ is ____________.

(Take $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )