An infinitely long thin wire, having a uniform charge density per unit length of 5nC/m, is passing through a spherical shell of radius 1 m, as shown in the figure. A 10 nC charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is ____. [Given: In SI units 4πϵ01=9×109,ln2=0.7. Ignore the area pierced by the wire.]
Answer: 171
Solution
Due to the wire:
The potential difference due to an infinite line charge with linear charge density λ=5 nC/m:
VR−VP=−∫0.52x2kλdx=−2kλln0.52
=−2×9×109×5×10−9×ln4=−90×2×0.7=−126 V
Due to the spherical shell:
With charge Q=10 nC and radius R=1 m:
VR−VP=2kQ−1kQ=−2kQ=−29×109×10×10−9=−45 V
Total:
VR−VP=−126−45=−171 V
∣VP−VR∣=171 V
JEE Advanced · 2024 · 26 May 2024 · Paper 2 · Integer answer
