To find the value of ( g_2 ) in this context, we can assume that ( g_1 ) and ( g_2 ) are charges, and the force ( F ) between them is given by Coulomb's law:
[
F = k \frac{|g_1 \cdot g_2|}{r^2}
]
Where:
- ( F ) is the force between the charges (given as ( 200 \times 10^{-3} ) N)
- ( g_1 ) is the first charge (given as ( 5 \times 10^{-9} ) C)
- ( g_2 ) is the second charge (which we need to find)
- ( r ) is the distance between the charges (given as ( 0.03 ) m)
- ( k ) is Coulomb's constant (given as ( 9 \times 10^9 , \text{N m}^2/\text{C}^2 ))
Let's rearrange the equation for ( g_2 ):
[
F = k \frac{|g_1 \cdot g_2|}{r^2} \implies |g_2| = \frac{F \cdot r^2}{k \cdot |g_1|}
]
Now, substituting in the values:
- ( F = 200 \times 10^{-3} = 0.2 , \text{N} )
- ( r = 0.03 , \text{m} )
- ( k = 9 \times 10^9 , \text{N m}^2/\text{C}^2 )
- ( g_1 = 5 \times 10^{-9} , \text{C} )
Now we can compute ( |g_2| ):
[
|g_2| = \frac{0.2 \cdot (0.03)^2}{9 \times 10^9 \cdot (5 \times 10^{-9})}
]
Calculating the numerator first:
[
0.2 \cdot (0.03)^2 = 0.2 \cdot 0.0009 = 0.00018
]
Now calculating the denominator:
[
9 \times 10^9 \cdot (5 \times 10^{-9}) = 9 \times 5 = 45 , \text{N m}^2/\text{C}
]
Now, we can find ( |g_2| ):
[
|g_2| = \frac{0.00018}{45} \approx 4 \times 10^{-6} , \text{C}
]
So, ( g_2 \approx 4 \times 10^{-6} , \text{C} ).
