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Three charges each equal to +4nC are pla...

Three charges each equal to +4nC are placed at the three comers of a square of side 2 cm. Find the electric field at the fourth corner.

Text Solution

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The elecrtic field due to charges at A, B & C can be calculated at point D as.
`E_A=Q_A/(4piepsilon_0r^2)=(9xx10^9xx4xx10^(-9))/(2xx10^(-2))^2=9xx10^4 NC^(-1)` along AD
`E_C=Q_C/(4piepsilon_0r^2)=(9xx10^9xx4xx10^(-9))/(2xx10^(-2))^2 =9xx10^4 NC^(-1)` along CD
`E_B=Q_B/(4piepsilon_0r^2) =(9xx10^9xx4xx10^(-9))/(2sqrt2xx10^(-2))^2 =4.5xx10^4 NC^(-1)` along BD

Resultant of `E_A` and `E_C` at D `E_D=sqrt(E_A^2+E_C^2)=sqrt(162xx10^8)`
`=12.73xx10^4 NC^(-1)`
Total field at D due to all the charges
`E_D+E_B=12.73xx10^4+4.5xx10^4=17.23xx10^4 NC^(-1)`
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