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kakasveta [241]
3 years ago
14

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a −3.0-μC charge

. Find the magnitude of the electric field at the center of the square. (k=1/4πϵ0=8.99×109 N.m^2/C^2)

Physics
2 answers:
PolarNik [594]3 years ago
5 0

Answer:

E=4.32\times 10^{5}\ N.C^{-1}

Explanation:

Given:

  • charges at the each of the three corner of a square, q_1=q_2=q_3=+3\times 10^{-6}\ C
  • side of the square, a=0.5\ m
  • charge at the remaining corner of the square, q_4=-3\times 10^{-6}\ C

<u>Distance of the center of the square from each of the vertex of square:</u>

Using Pythagoras theorem:

d^2+d^2=a^2

2d^2=0.5^2

d=0.3536\ m

As there two equal like charges at an equal distance on the opposite ends of a diagonal so they will cancel out the effect of field due to each other.

<u>Electric field at the center of the square due to </u>q_4<u>:</u>

E_4=\frac{1}{4\pi.\epsilon_0} \times \frac{q_4}{d^2}

E_4=9\times 10^9\times\frac{3\times 10^{-6}}{0.125}

E_4=216\times10^{3}\ N.C^{-1}

The charge on the opposite vertex will have the equal effect in the same direction which is towards the charge q_4. (refer the attached schematic)

<u>So, the net electric field at the center:</u>

E=2\times E_4

E=2\times 216\times 10^3

E=4.32\times 10^{5}\ N.C^{-1}

kramer3 years ago
3 0

Answer:

E = 440816.32 N/C

Explanation:

Given data:

Three point charge of charge equal to +3.0 micro coulomb

fourth point charge = - 3.0 micro coulomb

side of square = 0.50 m

K =1/4 \pi \epsilon_0 = 8.99 \times 10^9 N.m^2/c^2

Due to having equal charge on center of square, 2 charge produce equal electric field at center and other two also produce electric field at center of same value

So we have

E_1 + E_3 = 0

E =E_2 + E_4

E = 2 E_2

[E_2 =\frac{2\times k \times q}{r^2}

[r= \frac{(0.5^2 + 0.5^2)^2}{2} = 0.35 m]

plugging all value

E = 2 E_2

E = 2 E_2 =\frac{2\times k \times q}{r^2}

E = \frac{2 \times 8.99 \times 10^93\times 10^{-6}}{0.35^2}

E = 440816.32 N/C

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