1
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1 Two electric dipoles of dipole moments $$1.2 \times 10^{-30} \,\mathrm{Cm}$$ and $$2.4 \times 10^{-30} \,\mathrm{Cm}$$ are placed in two different uniform electric fields of strengths $$5 \times 10^{4} \,\mathrm{NC}^{-1}$$ and $$15 \times 10^{4} \,\mathrm{NC}^{-1}$$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $$\frac{1}{x}$$. The value of $$x$$ is __________.

2
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1 A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}$$ from its axis is ________ $$\mathrm{Vm}^{-1}$$. 3
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1 Three point charges of magnitude $$5 \mu \mathrm{C}, 0.16 \mu \mathrm{C}$$ and $$0.3 \mu \mathrm{C}$$ are located at the vertices $$A, B, C$$ of a right angled triangle whose sides are $$A B=3 \mathrm{~cm}, B C=3 \sqrt{2} \mathrm{~cm}$$ and $$C A=3 \mathrm{~cm}$$ and point $$A$$ is the right angle corner. Charge at point $$\mathrm{A}$$ experiences ____________ $$\mathrm{N}$$ of electrostatic force due to the other two charges.

4
JEE Main 2022 (Online) 25th July Morning Shift
Numerical
+4
-1 The volume charge density of a sphere of radius $$6 \mathrm{~m}$$ is $$2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$\times 10^{10} \,\mathrm{NC}^{-1}$$.

[Given : Permittivity of vacuum $$\epsilon_{0}=8.85 \times 10^{-12} \,\mathrm{C}^{2}\, \mathrm{~N}^{-1}-\mathrm{m}^{-2}$$ )

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