JEE Mains · Physics · STD 12 - 1. Electric charges and fields
An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.
- A \(16\)
- B \(20\)
- C \(23\)
- D \(30\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\(\frac{\mathrm{E}_S}{\mathrm{E}_{\ell}}=\frac{\sigma}{2 \epsilon_0} \times \frac{2 \pi \epsilon_0 \mathrm{r}}{\lambda}\) \(=\frac{\pi \times \sigma \mathrm{r}}{\lambda}\) \(=\frac{\pi \times 2 \lambda \times 2}{\lambda}=\frac{4 \pi}{1}\) \(\therefore \mathrm{n}=16\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at \(30°\) and \(90°\), respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at \(60°\) with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.JEE Mains 2026 Hard
- An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :JEE Mains 2023 Medium
- A swimmer wants to cross a river from point \(A\) to point \(B\). Line \(A B\) makes an angle of \(30^{\circ}\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line \({AB}\) should be \(^{\circ}\), so that the swimmer reaches point \({B}\).
JEE Mains 2021 Medium - A bi convex lens of focal length \(10\,cm\) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is \(...........\,D\).JEE Mains 2023 Medium
- In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \(P_1\) and \(P_2\) are orthogonal to each other. The polarizer \(P_3\) covers both the slits with its transmission axis at \(45^{\circ}\) to those of \(P_1\) and \(P_2\). An unpolarized light of wavelength \(\lambda\) and intensity \(I_0\) is incident on \(P_1\) and \(P_2\). The intensity at a point after \(P_3\) where the path difference between the light waves from \(s_1\) and \(s_2\) is \(\frac{\lambda}{3}\), is _______.
JEE Mains 2025 Hard - A particle of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) has an initial velocity \(\overline{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{j}} .\) If an electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}\) and magnetic field \(\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{i}}\) act on the particle, its speed will double after a time:JEE Mains 2020 Medium
More PYQs from JEE Mains
- If \(z=x+i y, x y \neq 0\), satisfies the equation \(z^2+i \bar{z}=0\), then \(\left|z^2\right|\) is equal to :JEE Mains 2024 Medium
- Let \(P Q R\) be a triangle with \(R(-1,4,2)\). Suppose \(M(2,1,2)\) is the mid point of \(PQ\). The distance of the centroid of \(\triangle \mathrm{PQR}\) from the point of intersection of the line \(\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}\) and \(\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}\) isJEE Mains 2024 Medium
- The ratio of de-Broglie wavelength of an \(\alpha\)-particle and a proton accelerated from rest by the same potential is \(\frac{1}{\sqrt{ m }}\), the value of \(m\) is \(........\)JEE Mains 2023 Easy
- If \(A\) and \(B\) are any two events such that \(P\left( A \right)\, = \frac{2}{5}\) and \(P\left( {A \cap \,B} \right)\, = \frac{3}{{20}},\) then the conditional probability, \(P\left( {A\,|\,A'\, \cup \,B')} \right),\) where \(A'\) denotes the complement of \(A,\) is equal toJEE Mains 2016 Hard
- \(1\, + \,\frac{{{1^3}\, + \,{2^3}}}{{1 + 2}} + \frac{{{1^3}\, + \,{2^3} + {3^3}}}{{1 + 2 + 3}} + ...... + \frac{{{1^3}\, + \,{2^3} + {3^3} + ..... + {{15}^3}}}{{1 + 2 + 3 + ..... + 15}} - \frac{1}{2}\left( {1 + 2 + 3 + ....+15} \right)\) is equal toJEE Mains 2019 Hard
- Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?JEE Mains 2025 Easy