Question

Three charges each 6C are placed at the corners A,B and C of a square ABCD of side 3m. Find the magnitude of the electric intensity at the corner D.​

Answer 1

Answer:do in the same way

Answer 2

Given ;

Three charges are placed at three corners of a square ABCD at corners A, B and c.

Magnitude of each charges :

q= 6 C

Side length of square :

s =3 m

To Find ;

Magnitude of electricity field intensity at corner D= ?

Solution :

∴We know that formula for electric field at any point at a distance r due to a point charge q is :

$E=\frac{Kq}{r^{2} }$

Distance of A from D :

= 3 m

And also the distance of C from D :

= 3 m

Distance of B from D :

=$\sqrt{2}\times 3$ m

∴The magnitude of E due to charges at A and C are equal and this is :

$E=K\times \frac{6}{3^{2} }$

And the magnitude of E due to charge at C is :

$E=K\frac{6}{(\sqrt{2}\times 3) ^{2} } \\\\E=K\frac{6}{2\times3^{2} }$

Resultant of E at D due to A and C is :

$E_{AC}=\sqrt{E_{A}^{2} + E_{B}^{2} } \\\\E_{AC}=\sqrt{2} \times K\frac{6}{3^{2} }$

Finally the net  E at D due to A , B and c will be :

$E_{net}= E_{AC}+ E_{B}\\E_{net}= K (\sqrt{2} \times \frac{6}{9} + \frac{1}{\sqrt{2} }\times \frac{6}{9} )\\\\E_{net}=K\times \frac{6}{9} \times (\sqrt{2} +\frac{1}{\sqrt{2} } )\\\\E_{net}=\sqrt{2} k$

$E_{net}= \sqrt{2} \times 9\times 10^{9} \\E_{net}=1.27\times 10^{10} \frac{N}{C}$

So finally the net electric field at D due to three charges at corners A, B and C is $1.27 \times 10^{10}$$1.27\times 10^{10}$