The charges +5 `mu`C and +10 `mu`C are placed 20 cm apart. The electric field at the mid point between the two charges is

Options

A. `4.5 xx 10^(6)` N/C directed towards + 5 `mu`C
B. `4.5 xx 10^(6)` N/C directed towards +10 `mu`C
C. `13.5 xx 10^(6)` N/C directed towards + 5 `mu`C
D. `13.5 xx 10^(6)` N/C directed towards + 10 `mu`C

Answer

(a)

Explanation

Electric field at mid point due charges `q_(1)` and `q_(2)`,`:. E = E_(2) - E_(1)`
`= 1/4 pi epsilon_(0) q_(2)/(r/2)^(2) - 1/4 pi epsilon_(0) q_(1)/(r/2)^(2)[q_(2)- q_(1)] `
`= 9xx10^(9)xx4/(20xx10^(-2))^(2)[10xx10^(-6) - 5 xx 10^(-6)]`
= `4.5 xx 10^(6)N//C`