Two charges of 1 micro C and - 1 micro C are placed at the corners of the base of an equilibrium triangle. The length of the side of the triangle is 0.7 metre.Find the electric field intensity at the apex of the triangle.?

Question

Two charges of  1 micro C and - 1 micro C are placed at the corners of the base of an equilibrium triangle. The length of the side of the triangle is 0.7 metre.Find the electric field intensity at the apex of the triangle.?

Answer

Problem Statement:

Two charges of 1 micro C and -1 micro C are placed at the corners of the base of an equilibrium triangle. The length of the side of the triangle is 0.7 metre. Find the electric field intensity at the apex of the triangle.

Solution:

Electric Field Intensity:

The Electric Field Intensity at a point is defined as the force experienced per unit positive charge at that point.

Mathematically, Electric Field Intensity (E) = F/Q, where F is the force experienced and Q is the charge.

Equilibrium Triangle:

An Equilibrium Triangle is a triangle in which all the forces acting on the charges are balanced and the net force experienced by the charges is zero.

Let us consider the following diagram:

Electric Field at Apex:

Let us consider a point P at the apex of the triangle. The electric field at point P due to the charge Q1 can be calculated using Coulomb's Law.

Mathematically, the Electric Field at P due to Q1 (E1) = (1/4πε) * (Q1/r1^2), where ε is the permittivity of the medium, Q1 is the charge on Q1, and r1 is the distance between Q1 and P.

Similarly, the Electric Field at P due to Q2 (E2) = (1/4πε) * (Q2/r2^2), where Q2 is the charge on Q2, and r2 is the distance between Q2 and P.

Since the triangle is an equilibrium triangle, the net electric field at P due to Q1 and Q2 is zero.

Mathematically, E1 + E2 = 0, which implies that (Q1/r1^2) = -(Q2/r2^2).

Also, since the triangle is equilateral, r1 = r2 = 0.7/√3 metre.

Therefore, (Q1/(0.7/√3)^2) = -(Q2/(0.7/√3)^2).

Substituting the values of Q1 and Q2, we get:

(1/(0.7/√3)^2) = -(-1/(0.7/√3)^2).

Therefore, the Electric Field at point P due to Q1 and Q2 is zero.

Conclusion:

Hence, the Electric Field Intensity at the apex of the equilibrium triangle is zero.

Answer

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