Question

Ten charges having charge $1\mu C,8\mu C,27\mu C,.......1000\mu C$ are placed on the x-axis with co-ordinates $x=1m,2m,3m,4m,.....10m.$ The net electric field intensity at the origin is:

• A. $9\times {10}^{5}N/C$
• B. $9\times {10}^{4}N/C$
• C. $4.95\times {10}^{-5}N/C$
• D. $4.95\times {10}^{5}N/C$

Answer 1

Answer: (A)

$9\times {10}^{5}N/C$

The net field due to the point charges is the sum of all the electric fields.

$E=K\left[\frac{1}{1}+\frac{8}{2}+\frac{27}{9}+.......+\frac{1000}{100}\right]\times {10}^{-6}$

$=9\times {10}^9\times {10}^{-6}\left[1+2+3+4+......+10\right]$

$=9\times {10}^9\times {10}^{-6}\times \frac{10\times 11}{2}$

$=4.5\times {10}^4\times 11$

$E_{net}=49.5\times {10}^{4}N/C$