Consider a point charges of 72 Q are placed at each corner of an equilateral triangle, which has...

Question:

Consider a point charges of 72 Q are placed at each corner of an equilateral triangle, which has sides of length 8 L. What is the magnitude of the electric field at the mid-point of any of the three sides of the triangle in units of {eq}kQ/L^2 {/eq}?

Electric field:

The current generates an electromagnetic field around the region where it passes in the conductor. The generated fields are electric field and magnetic field which attracts similar charges and repels with force on the dissimilar charge.

Answer and Explanation:

Given data

  • The value of the point charge is {eq}q = 72Q {/eq}
  • The value of the length of the equilateral triangle is {eq}a = 8L {/eq}


The expression for the electric field is

$$E = \dfrac{{kq}}{{{d_c}^2}} $$

Here the value of the {eq}{d_c} = \sqrt {{{\left( {8L} \right)}^2} - {{\left( {\dfrac{{8L}}{2}} \right)}^2}} {/eq}

Substitute the value in the above equation

$$\begin{align*} E &= \dfrac{{k \times 72Q}}{{{{\left( {\sqrt {{{\left( {8L} \right)}^2} - {{\left( {\dfrac{{8L}}{2}} \right)}^2}} } \right)}^2}}}\\ &= \dfrac{{k \times 72Q}}{{{{\left( {\sqrt {{{\left( {8L} \right)}^2} - {{\left( {\dfrac{{8L}}{2}} \right)}^2}} } \right)}^2}}}\\ &= \dfrac{{1.5kQ}}{{{L^2}}} \end{align*} $$

Thus the value of the electric field is in terms of {eq}\boxed{\dfrac{{kQ}}{{{L^2}}}} {/eq}


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