Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let P(r)=\frac{Q}{\pi R^{4}}r be the charge density distribution for a solid sphere of radius R and total charge Q . For a point 'p' insid

Let P(r)=\frac{Q}{\pi R^{4}}r  be the charge density distribution for a solid sphere of radius R and total charge Q . For a point 'p' insid

Answers (1)

Let us consider a spherical shell of thickness dx and radius x. The volume of this spherical shell =4 \pi r^{2} d r 

The charge enclosed within shell  =\frac{Q r}{\pi R^{4}}\left[4 \pi r^{2} d r\right] 

The charge enclosed in a sphere of radius r1 is

=\frac{4 Q}{R^{4}} \int_{0}^{r_{1}} r^{3} d r=\frac{4 Q}{R^{4}}\left[\frac{r^{4}}{4}\right]_{0}^{r}-1=\frac{Q}{R^{4}} r_{1}^{4} 

 

∴ The electric field at point p inside the sphere at a distance r1 from the centre of the sphere is

E=\frac{1}{4 \pi \in_{0}} \frac{\left[\frac{Q}{R^{4}} r_{1}^{4}\right]}{r_{1}^{2}}=\frac{1}{4 \pi \in_{0}} \frac{Q}{R^{4}} r_{1}^{2}

Posted by

Satyajeet Kumar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question