Two point charges +Q1 and -Q2 are placed it A and B respectively . A line of force emanantrs from Q1 at an angle θ with the like joining A and B . At what angle will it terminate at B ?
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We know that number of emerging lines of force is proportional to magnitude of the charge. The field likes emanating from Q₁ are spread out equally in all directions . The number of field likes or flux though cone of half angle θ is Q₁/4π × 2π(1-cosθ). similarly the number of lines of force terminating on -Q2 at an angle say ∅ is Q₂/4π × 2π(1-cos∅). The total likes of force emanating from Q₁ is equal to the total likes of force terminating on Q₂
=> Q₁/4π × 2π(1-cosθ) = Q₂/4π × 2π{1-cos∅)
or Q₁/2 × (1-cosθ) = Q₂/2 × (1-cos∅)
Q₁sin²(θ/2) = Q₂sin²(∅/2)
sin(∅/2) = √Q₁/Q₂ × sin(θ/2)
=> ∅ = 2sin-¹{√Q₁/Q₂ × sin(θ/2)}
=> Q₁/4π × 2π(1-cosθ) = Q₂/4π × 2π{1-cos∅)
or Q₁/2 × (1-cosθ) = Q₂/2 × (1-cos∅)
Q₁sin²(θ/2) = Q₂sin²(∅/2)
sin(∅/2) = √Q₁/Q₂ × sin(θ/2)
=> ∅ = 2sin-¹{√Q₁/Q₂ × sin(θ/2)}
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