Answer:
The electrical force between two balloons is 67.5N.
Explanation:
There are two charged balloons, let's say a and b.
The charge on the balloon a = [tex]Q_a = 3.0 * 10^{-6}[/tex]C
The charge on the balloon b = [tex]Q_b = 2.5 * 10^{-7}[/tex]C
Both balloons are 1 cm apart; it means that the distance r between the balloon a and the balloon b is 0.01 m (since 1 cm = 0.01 m).
We need to find the electrical force between them. By using the Coulomb's law, the magnitude of the electrical force between both the balloon is given as follows:
[tex]F = \frac{kQ_aQ_b}{r^2}[/tex] --- (A)
Where,
k = Coulomb's constant = [tex]\frac{1}{4\pi\epsilon_o}[/tex] = [tex]9 * 10^9 \frac{Nm^2}{C^2}[/tex]
Plug all the values in the equation (A):
[tex]F = \frac{(9*10^9)(3.0*10^{-6})(2.5*10^{-7})}{(0.01)^2} \\F = 67.5 N[/tex]
Hence, the electrical force between two balloons is 67.5N (three significant figures).
The magnitude of electrical force between them is about 68 Newton
Electric charge consists of two types i.e. positively electric charge and negatively electric charge.
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There was a famous scientist who investigated about this charges. His name is Coulomb and succeeded in formulating the force of attraction or repulsion between two charges i.e. :
[tex]\large {\boxed {F = k \frac{Q_1Q_2}{R^2} } }[/tex]
F = electric force (N)
k = electric constant (N m² / C²)
q = electric charge (C)
r = distance between charges (m)
The value of k in a vacuum = 9 x 10⁹ (N m² / C²)
Let's tackle the problem now !
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Given:
charge of balloon 1 = q₁ = 3.0 × 10⁻⁶ C
charge of balloon 2 = q₂ = 2.5 × 10⁻⁷ C
distance between balloon 1 and balloon 2 = R = 1 cm = 1 × 10⁻² m
Unknown:
electrical force between them = F = ?
Solution:
[tex]F = k \frac{q_1 q_2}{R^2}[/tex]
[tex]F = 9 \times 10^9 \times \frac{ 3.0 \times 10^{-6} \times 2.5 \times 10^{-7} }{ ( 1 \times 10^{-2} )^2 }[/tex]
[tex]F = 9 \times 10^9 \times \frac{ 7.5 \times 10^{-13} }{ 10^{-4} }[/tex]
[tex]F = 9 \times 10^9 \times 7.5 \times 10^{-9}[/tex]
[tex]F = 67.5 \texttt{ Newton}[/tex]
[tex]F \approx 68 \texttt { Newton}[/tex] → ( 2 Significant Figures )
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Grade: High School
Subject: Physics
Chapter: Static Electricity
Keywords: Series , Parallel , Measurement , Absolute , Error , Combination , Resistor , Resistance , Ohm , Charge , Small , Forces
