Question

There are three charges of magnitude 3uC,2 uC and 3uC are located at three cornersA,B and C of a square ABCD of each sides measuring 2m. Determine the net force on 2 uC charge.



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Answer 1

Answer:

F= 19.09 ×10⁻³ N direction DB

Explanation:

given

a square ABCD whose side 2 m

corner A have charge 3×10⁻⁶ C

B have charge  2×10⁻⁶ C

C have charge  3×10⁻⁶ C

find force on B

force on B due to A

F₁= k q₁q₂/r²

= k( 3×10⁻⁶ C× 2×10⁻⁶ C)/ 4

F₁= (3/2)k×10⁻¹² AB direction

force on B due to C

F₃= k q₂q₃/r²

= k( 3×10⁻⁶ C× 2×10⁻⁶ C)/ 4

F₁= (3/2)k×10⁻¹² CB direction

add F₁ and F₃

angle between F₁ and F₃  ∅=90°

net force

F=√ F₁² + F₃² + 2F₁F₃ cos∅

cos 90 = 0

F=√ F₁² + F₃²

F = √((3/2)k×10⁻¹²)²+((3/2)k×10⁻¹²)²

F = (3/2)k×10⁻¹²×√2

F = 13.5×10⁻³√2

F= 19.09 ×10⁻³ N