Three point charges $8 \times 10^{- 9} C, 32 \times 10^{- 9}$ C and $24 \times 10^{- 9} C$ are placed at the corners A,B, and C of a square ABCD having side 0.04 m. Calculate the magnitude of electric intensity at the corner D.

Open in App

Solution

$q_{A} = 8 \times 10^{- 9} C$
$q_{B} = 32 \times 10^{- 9} C$
$q_{C} = 24 \times 10^{- 9} C$
Electric field intensity at D: $E_{D} = \frac{k q_{A}}{r_{A D}^{2}} + \frac{k q_{B}}{r_{B D}^{2}} + \frac{k q_{C}}{r_{C D}^{2}}$ where $r_{A D}$ is the distance between A and D and so on..
$E_{D} = k (\frac{q_{A}}{r_{A D}^{2}} + \frac{q_{B}}{r_{B D}^{2}} + \frac{q_{C}}{r_{C D}^{2}})$
$= k (\frac{8 \times 10^{- 9}}{(0.4)^{2}} + \frac{32 \times 10^{- 9}}{2 \times (0.04)^{2}} + \frac{24 \times 10^{- 9}}{(0.04)^{2}}$ )
$= 9 \times 10^{9} \times 10^{- 9} \times \frac{8}{(0.04)^{2}} [1 + \frac{4}{2} + 3]$
$= 45000 \times [6]$
$= 270000 N / C$

Suggest Corrections

Similar questions

Two electric charges of $+ 10^{- 9} C$ and $- 10^{- 9} C$ are placed at the corners A and B of an equilateral triangle ABC side 5cm.The electric intensity at C is

Q. At the corners A, B and C of a square ABCD (each side 0.2 m) positive charges of 2

\times 10^{- 9}

c, 4

\times 10^{- 9}

C and 6

\times 10^{- 9}

C are placed. What is the intensity of the electric field at D?
(1836 N/C at 24 43' with CD produced)

Q. Three point charges of

3 \times 10^{- 9} C

are situated at each of three corners of a square, whose side is

15 c m

. The magnitude and direction of the electric field at the vacant corner of the square are:

Point charges of $3 \times 10^{- 9} C$ are situated at each of the three corners of a square whose side is $15 c m$ . The magnitude and direction of electric field at the vacant corner of the square is :

Q. A square of side

\sqrt{2}

m has charges of

+ 2 \times 10^{- 9} C,

1 \times 10^{- 9} C,

- 2 \times 10^{- 9} C,

and

- 3 \times 10^{- 9} C,

respectively at its corners. What is the potential at the centre of the square?

Join BYJU'S Learning Program

Three point charges 8×10−9C,32×10−9 C and 24×10−9C are placed at the corners A,B, and C of a square ABCD having side 0.04 m. Calculate the magnitude of electric intensity at the corner D.

qA=8×10−9CqB=32×10−9CqC=24×10−9CElectric field intensity at D:ED=kqAr2AD+kqBr2BD+kqCr2CD where rAD is the distance between A and D and so on..ED=k(qAr2AD+qBr2BD+qCr2CD)=k(8×10−9(0.4)2+32×10−92×(0.04)2+24×10−9(0.04)2)=9×109×10−9×8(0.04)2[1+42+3]=45000×[6]=270000N/C

Three point charges $8 \times 10^{- 9} C, 32 \times 10^{- 9}$ C and $24 \times 10^{- 9} C$ are placed at the corners A,B, and C of a square ABCD having side 0.04 m. Calculate the magnitude of electric intensity at the corner D.