1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_{0}$$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $$\mathrm{q}_{0}$$ executes $$\mathrm{SHM}$$. The time period of oscillation of charge $$\mathrm{q}_{0}$$ will be :

A
$$\sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}$$
B
$$\sqrt{\frac{q_{0} Q}{4 \pi^{3} \varepsilon_{0} m a^{3}}}$$
C
$$\sqrt{\frac{2 \pi^{2} \varepsilon_{0} m a^{3}}{q_{0} Q}}$$
D
$$\sqrt{\frac{8 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 An electron (mass $$\mathrm{m}$$) with an initial velocity $$\vec{v}=v_{0} i\left(v_{0}>0\right)$$ is moving in an electric field $$\vec{E}=-E_{0} \hat{i}\left(E_{0}>0\right)$$ where $$E_{0}$$ is constant. If at $$\mathrm{t}=0$$ de Broglie wavelength is $$\lambda_{0}=\frac{h}{m v_{0}}$$, then its de Broglie wavelength after time t is given by

A
$$\lambda_{0}$$
B
$$\lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)$$
C
$$\lambda_{0} t$$
D
$$\frac{\lambda_{0}}{\left(1+\frac{e E_{0} t}{m v_{0}}\right)}$$
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1 Two uniformly charged spherical conductors $$A$$ and $$B$$ of radii $$5 \mathrm{~mm}$$ and $$10 \mathrm{~mm}$$ are separated by a distance of $$2 \mathrm{~cm}$$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $$A$$ and $$B$$ will be :

A
1 : 2
B
2 : 1
C
1 : 1
D
1 : 4
4
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1 Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :

A
x = d
B
$$x = {d \over 2}$$
C
$$x = {d \over {\sqrt 2 }}$$
D
$$x = {d \over {2\sqrt 2 }}$$
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