Question 4 Two point charges, \( 2.5 \times 10-6 \mathrm{C} \) and \( -5.0 \times 10-6 \mathrm{C} \), are placed 3.0 m apart. What is the magnitude of the electric field at point \( P \), midway between the two charges? \( 2.5 \times 10^{-6} \mathrm{C} \)

To find the electric field at point \( P \), we can use the formula for the electric field due to a point charge: \[ E = \frac{k |q|}{r^2} \] where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), \( q \) is the charge, and \( r \) is the distance from the charge to point \( P \). In this case, each charge is 1.5 m away from point \( P \). First, calculate the electric field due to the positive charge: \[ E_1 = \frac{(8.99 \times 10^9)(2.5 \times 10^{-6})}{(1.5)^2} \] Next, calculate the electric field due to the negative charge: \[ E_2 = \frac{(8.99 \times 10^9)(5.0 \times 10^{-6})}{(1.5)^2} \] Since the electric field due to the negative charge points toward the charge, while the electric field from the positive charge points away from it, we have: \[ E_{net} = E_1 - E_2 \] Calculating both fields gives you the net electric field at point \( P \). You know the famous tale of Benjamin Franklin and his kite experiment in the 1700s? Well, he wasn't just flying kites for fun! He was actually demonstrating the principles of electricity, including how electric charges interact. Franklin’s experiments on charged objects laid the groundwork for what we now understand about electric fields. Charged objects, like the ones in our problem, are everywhere—so it’s worth knowing their history! Ever found yourself tangled in a web of numbers while calculating electric fields? You're not alone! Many folks miscalculate by forgetting to use absolute values for charges or mishandling the distance squared. Always keep an eye on where you're measuring from; that pesky \( r^2 \) is often where errors sneak in. To keep things clear, draw a quick sketch of the situation to visualize charge interactions—trust me, it saves you from a lot of future headaches!