Electrostatics 2 Question 10

10. A charge Q is uniformly distributed over a long rodAB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is

(2013 Main)

(a) Q8πε0L

(b) 3Q4πε0L

(c) Q4πε0Lln2

(d) Qln24πε0L

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Answer:

Correct Answer: 10. (c)

Solution:

V=L2LkdQx=L2LkQLdxx=Q4πε0LL2L1xdx=Q4πε0L[logex]L2L=Q4πε0L[loge2LlogeL]=Q4πε0Lln(2)

11. For inside points (rR)

E=0V= constant =14πε0qR

For outside points (rR)

 and E=14πε0qr2 or E1r2 an =14πε0qr or V1r

On the surface (r=R)

V=14πε0qRE=14πε0qR2=σε0

where, σ=q4πR2= surface charge density corresponding to above equations the correct graphs are shown in option (d).



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