Electrostatics Question 770
Question: A point charge of magnitude $ +1\mu C $ is fixed at (0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the center of the sphere is:
Options:
A) $ 1.8\times 10^{5}V\text{ and }-5.625\times 10^{6}V/m $
B) 0 V and 0 V/m
C) $ 2.25\times 10^{5}V\text{ and }-5.625\times 10^{6}V/m $
D) $ 2.25\times 10^{5}V\text{ and 0 V/m} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ q=1\mu C=1\times {{10}^{-6}},r=4cm=4\times {{10}^{-2}}m $
Potential $ V=\frac{kg}{r}=\frac{9\times 10^{8}\times {{10}^{-6}}}{4\times {{10}^{-2}}} $
$ =2.25\times 10^{5}V. $
Induced electric field $ E=-\frac{kq}{r^{2}} $
$ =\frac{9\times 10^{9}\times 1\times {{10}^{-6}}}{16\times {{10}^{-4}}}=5.625\times 10^{6}V/m $
