What is the electric force acting between two charges of 0.0072 C and -0.0060 C that are 0.0040 m apart? Use [tex]F_0=\frac{k q_1 q_2}{r^2}[/tex] and [tex]k =9.00 \times 10^9 N \cdot m ^2 / C ^2[/tex].
A. [tex]$-9.7 \times 10^7 N$[/tex]
B. [tex]$2.4 \times 10^{-10} N$[/tex]
C. [tex]$9.7 \times 10^7 N$[/tex]
D. [tex]$-2.4 \times 10^{-10} N$[/tex]
Answer (1)
Calculate the electric force using Coulomb's law: F = r 2 k q 1 q 2 .
Substitute the given values: k = 9.00 × 1 0 9 N × m 2 / C 2 , q 1 = 0.0072 C , q 2 = − 0.0060 C , and r = 0.0040 m .
Compute the electric force: F = ( 0.0040 ) 2 ( 9.00 × 1 0 9 ) × ( 0.0072 ) × ( − 0.0060 ) = − 2.43 × 1 0 10 N .
The calculated electric force is − 2.43 × 1 0 10 N .
Explanation
Problem Setup and Given Data We are given two charges, q 1 = 0.0072 C and q 2 = − 0.0060 C, separated by a distance r = 0.0040 m. We are also given Coulomb's constant k = 9.00 × 1 0 9 N × m 2 / C 2 . Our goal is to calculate the electric force F between these charges using the formula F = r 2 k q 1 q 2 .
Substituting Values Now, we substitute the given values into the formula: F = ( 0.0040 m ) 2 ( 9.00 × 1 0 9 N × m 2 / C 2 ) × ( 0.0072 C ) × ( − 0.0060 C )
Calculating the Force Let's calculate the force: F = ( 0.0040 ) 2 ( 9.00 × 1 0 9 ) × ( 0.0072 ) × ( − 0.0060 ) = 0.000016 − 388800 = − 24300000000 N = − 2.43 × 1 0 10 N
Comparing with Options and Final Answer Comparing our calculated value with the given options, we see that the closest answer is − 2.43 × 1 0 10 N . However, the options are given in terms of 1 0 7 N and 1 0 − 10 N . Let's re-evaluate the calculation to match one of the options. The calculation is correct, so there might be a typo in the options. The closest option to our result is A. − 9.7 × 1 0 7 N if we consider the order of magnitude, but the correct calculation yields − 2.43 × 1 0 10 N . Since we must choose from the given options, and given that the correct calculation is − 2.43 × 1 0 10 N , there seems to be an error in the provided options. However, if we are to choose the closest one, we should re-examine our calculation. We have: F = ( 9.00 × 1 0 9 ) × ( 0.0072 ) × ( − 0.0060 ) / ( 0.0040 ) 2 = − 2.43 × 1 0 10 N
Since none of the options match the correct calculation, it is possible there was a typo in the question or the options. However, based on the calculation, the electric force is − 2.43 × 1 0 10 N .
Examples
Electric force calculations are crucial in designing electronic devices, understanding material properties, and developing technologies like electrostatic painting and printing. For instance, in inkjet printers, charged ink droplets are precisely controlled by electric fields to form high-resolution images on paper. Similarly, electrostatic precipitators use electric forces to remove particulate matter from exhaust gases, contributing to air pollution control. These applications demonstrate how understanding and applying electric force principles directly impact technological advancements and environmental protection.
