4 equal point charges each of 16 micro coulomb are placed on the 4 corners of the square of side 0.2 m. Calculate the force experienced by any one of the charge
Answers
Let ABCD is square of side length 0.2m and four equal point charge each of 16 micro coulomb are placed on the four corner A, B, C and D of the square.
we have to find force experienced by anyone of the charge . we take point A, we have to find force experienced by point A.
to understand see diagram,
force exerted by B on A = Kq²/a²
where q = 16 microcoulomb, a = 0.2m
force exerted by C on A = Kq²/(√2a)² = Kq²/2a²
force exerted by D on A = Kq²/a²
now, resultant of force exerted by B and D on A = √{(Kq²/a²)² + (Kq²/a²)²}= √2Kq²/a² , it is along CA .
now, net force experienced by A = resultant of force exerted by B and D on A + force exerted by C on A
= √2Kq²/a² + Kq²/2a²
= (√2 + 1/2)Kq²/a²
= (2√2 + 1)Kq²/2a²
now, putting k = 9 × 10^9 Nm²/C² , q = 16 × 10^-6 C and a = 0.2 m
= (2√2 + 1) × 9 × 10^9 × (16 × 10^-16)²/2(0.2)²
= (2√2 + 1) × 9 × 256 × 10^-3/(0.08)
= (2√2 + 1) × 9 × 32 × 10^-1
= 110.258 N along CA
Answer:
Explanation:
Let ABCD is square of side length 0.2m and four equal point charge each of 16 micro coulomb are placed on the four corner A, B, C and D of the square.
we have to find force experienced by anyone of the charge . we take point A, we have to find force experienced by point A.
to understand see diagram,
force exerted by B on A = Kq²/a²
where q = 16 microcoulomb, a = 0.2m
force exerted by C on A = Kq²/(√2a)² = Kq²/2a²
force exerted by D on A = Kq²/a²
now, resultant of force exerted by B and D on A = √{(Kq²/a²)² + (Kq²/a²)²}= √2Kq²/a² , it is along CA .
now, net force experienced by A = resultant of force exerted by B and D on A + force exerted by C on A
= √2Kq²/a² + Kq²/2a²
= (√2 + 1/2)Kq²/a²
= (2√2 + 1)Kq²/2a²
now, putting k = 9 × 10^9 Nm²/C² , q = 16 × 10^-6 C and a = 0.2 m
= (2√2 + 1) × 9 × 10^9 × (16 × 10^-16)²/2(0.2)²
= (2√2 + 1) × 9 × 256 × 10^-3/(0.08)
= (2√2 + 1) × 9 × 32 × 10^-1
= 110.258 N along CA
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