JEE Mains · Physics · STD 12 - Electric charges and fields
- JEE Mains 2024
- Hard
- Numerical
An electric field, \(\overrightarrow{\mathrm{E}}=\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^2\) area having unit vector \(\hat{\mathrm{n}}=\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)\). The electric flux for that surface is _______ \(\mathrm{Vm}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
\(\phi =\overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{A}}\)
\(=\left(\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}\right) \cdot 4\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)\)
\(=\frac{4}{6} \times(4+6+8)=12 \mathrm{Vm}\)
More questions from Physics
- For the given circuit, the power across zener diode is ..... \({mW}.\)
JEE Mains 2021 Hard - If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 {x}} \;{m} / {s}\), then the acceleration of the body is \(\ldots \ldots {m} / {s}^{2}\)JEE Mains 2021 Hard
- If mass is written as \(\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\) then the value of \(P\) will be _______. (Constants have their usual meaning with \(\mathrm{k}\) a dimensionless constant)JEE Mains 2024 Hard
- A thin uniform rod of length \(2\,m\). cross sectional area ' \(A\) ' and density ' \(d\) ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity \(\omega\). If value of \(\omega\) in terms of its rotational kinetic energy \(E\) is \(\sqrt{\frac{\alpha E}{ Ad }}\) then the value of \(\alpha\) is \(...........\)JEE Mains 2023 Medium
- Match List \(- I\) (Electromagnetic wave type) with List \(- II\) (Its association/application) and select the correct option from the choices given below the lists
\(a\) \(b\) \(c\) \(d\)લિસ્ટ\(-I\) લિસ્ટ\(-II\) \(a\). Infrared waves \(i\). To treat muscular strain \(b\). Radio waves \(ii\). For broadcasting \(c\). \(X-\)rays \(iii\). To detect fracture of bones \(d\). Ultraviolet rays \(iv\). Absorbed by the ozone layer of the atmosphere JEE Mains 2014 Medium - A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______.JEE Mains 2024 Hard
More PYQs from JEE Mains
- A \(70\, kg\) man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force \(F\) to raise himself The center of gravity rises by \(0.5\, m\) before he leaps. After the leap the \(c.g.\) rises by another \(1\, m\). The maximum power delivered by the muscles is : (Take \(g\, = 10\, ms^{-2}\))JEE Mains 2013 Hard
- A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just \(10 \%\) of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is.....\(^o\)JEE Mains 2020 Medium
- A simple pendulum of mass \('m',\) length \('I'\) and charge \('+q'\) suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be -
JEE Mains 2021 Hard - Two materials having coefficients of thermal conductivity \(3K\) and \(K\) and thickness \(d\) and \(3d\), respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are \(\theta_2\) and \(\theta_1\) respectively \(\left( {\theta _2} > {\theta _1} \right)\) . The temperature at the interface is
JEE Mains 2019 Medium - A car is moving with a constant speed of \(20\,m / s\) in a circular horizontal track of radius \(40\,m\). A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take \(g =10\) \(\left.m / s ^2\right)\)JEE Mains 2023 Medium