Been there, done that. You are correct and the book is wrong. See discussion here.KnightTheConqueror said:
Thank you, i just started electromagnetism and i got disappointed that perhaps I'm not getting proper grasp of the concepts. Thanks for clarifying the book is wrongkuruman said:
I wish you success with your studies. If you need more help, you know where to find it.KnightTheConqueror said:
To calculate the electrostatic force between two point charges, you can use Coulomb's Law. The formula is \( F = k_e \frac{|q_1 q_2|}{r^2} \), where \( F \) is the magnitude of the force, \( k_e \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.
The direction of the electrostatic force depends on the signs of the charges. If both charges are of the same sign (both positive or both negative), they repel each other, and the force vectors point away from each other. If the charges are of opposite signs, they attract each other, and the force vectors point towards each other.
For multiple charges, you need to calculate the force exerted on the charge of interest by each of the other charges individually using Coulomb's Law, and then use vector addition to find the net force. This involves breaking the forces into their components, summing the components, and then finding the resultant vector.
The sign of the charges affects the direction of the force but not its magnitude. In Coulomb's Law, the absolute values of the charges are used to determine the magnitude of the force, while the signs determine whether the force is attractive or repulsive.
For continuous charge distributions, you need to use integration. Divide the charge distribution into infinitesimal elements, calculate the force due to each element using Coulomb's Law, and then integrate these forces over the entire charge distribution. This often involves setting up and solving an integral that accounts for the geometry and distribution of the charge.