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Saturday, 31 October

JEE Main 2022 · PhysicsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Physics Q40

Question 40 of 90 in this shift, Physics question 10 of 30, Section A.

A spherically symmetric charge distribution is considered with charge density varying as ρ(r)={ρ0(34−rR)for r≤Rzerofor r>R\rho(r) = \begin{cases} \rho_0\left(\frac{3}{4} - \frac{r}{R}\right) & \text{for } r \le R \\ \text{zero} & \text{for } r > R \end{cases} Where, r(r < R) is the distance from the centre O (as shown in figure). The electric field at point P will be :

The figure, in words

A circle of radius R labelled ρ(r)\rho(r) with centre O; point P inside at distance r from O.
  1. (1)ρ0r4ϵ0(34−rR)\frac{\rho_0 r}{4\epsilon_0}\left(\frac{3}{4} - \frac{r}{R}\right)
  2. (2)ρ0r3ϵ0(34−rR)\frac{\rho_0 r}{3\epsilon_0}\left(\frac{3}{4} - \frac{r}{R}\right)
  3. (3)ρ0r4ϵ0(1−rR)\frac{\rho_0 r}{4\epsilon_0}\left(1 - \frac{r}{R}\right)Official answer
  4. (4)ρ0r5ϵ0(1−rR)\frac{\rho_0 r}{5\epsilon_0}\left(1 - \frac{r}{R}\right)

Official answer

Option 3

NTA final key.

Chapter
Electric Charges and Fields
Topic
Gauss's Law
Idea tested
Field of Non-uniform Spherical Charge

Same topic in other shifts

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.