Three charges (q1 = 8.7 nC, q2 = -7.2 nC, and q3 = -4.8 nC) are at the corners of a square of side a = 9.2 cm, as shown in the picture. Determine the magnitude of the resultant electric force on each charge.
q1, q2, q3 –from the lower left corner – counterclockwise.
Origin of the coordinate system is at the corner where q1 is located.
F12=k•q1•q2/a² =
=9•10^9•8.7•10^-9•7.2•10^-9/9.2²•10^-4=
= 6.74•10^-5 N
F12x=0 F12y=6.74•10^-5 N.
F13=k•q1•q3/D(a√2)² =
=9•10^9•8.7•10^-9•4.8•10^-9/9.2²•10^-4•1.41=
=3.15•10^-5 N
F13x=F13y=3.15•10^-5•cos45=2.23•10^-5 N.
F1x= F12x+ F13x =0+2.23•10^-5 =2.23•10^-5 N.
F1y= F12y+ F13y= 6.74•10^-5 +2.23•10^-5 =8.97•10^-5 N.
F1=sqrt(F1x² + F1y²) =sqrt(2.23² +8.97²)•10^-5 =9.24•10^-5 N
The same procedure for other charges
Order, clockwise- q1, q2, q3....
Could you explain the procedure in words?
Never mind Elena, when I wrote it out on paper it made sense. Thank you very much! :)
To determine the magnitude of the resultant electric force on each charge, we need to calculate the net electric force exerted on each charge due to the other two charges.
The electric force between two charges is given by Coulomb's Law, which states that the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the equation:
F = (k * |q1 * q2|) / r²
Where:
k = Coulomb's constant (k = 9 × 10^9 N m²/C²)
Let's calculate the net electric force on each charge:
For q1:
The net electric force on q1 is the vector sum of the forces acting on it due to q2 and q3.
F₁₂ = (k * |q1 * q2|) / r² = (9 × 10^9 N m²/C²) * |(8.7 × 10^-9 C) * (-7.2 × 10^-9 C) / (0.092 m)²|
F₁₃ = (k * |q1 * q3|) / r² = (9 × 10^9 N m²/C²) * |(8.7 × 10^-9 C) * (-4.8 × 10^-9 C) / (0.092 m)²|
The magnitude of the net electric force on q1 is given by:
|F₁net| = √(|F₁₂|² + |F₁₃|²)
For q2:
The net electric force on q2 is the vector sum of the forces acting on it due to q1 and q3.
F₂₁ = (k * |q2 * q1|) / r² = (9 × 10^9 N m²/C²) * |(-7.2 × 10^-9 C) * (8.7 × 10^-9 C) / (0.092 m)²|
F₂₃ = (k * |q2 * q3|) / r² = (9 × 10^9 N m²/C²) * |(-7.2 × 10^-9 C) * (-4.8 × 10^-9 C) / (0.092 m)²|
The magnitude of the net electric force on q2 is given by:
|F₂net| = √(|F₂₁|² + |F₂₃|²)
For q3:
The net electric force on q3 is the vector sum of the forces acting on it due to q1 and q2.
F₃₁ = (k * |q3 * q1|) / r² = (9 × 10^9 N m²/C²) * |(-4.8 × 10^-9 C) * (8.7 × 10^-9 C) / (0.092 m)²|
F₃₂ = (k * |q3 * q2|) / r² = (9 × 10^9 N m²/C²) * |(-4.8 × 10^-9 C) * (-7.2 × 10^-9 C) / (0.092 m)²|
The magnitude of the net electric force on q3 is given by:
|F₃net| = √(|F₃₁|² + |F₃₂|²)
By calculating these values, you can determine the magnitude of the resultant electric force on each charge.