Two point charges of equal magnitude are 8cm apart. at the midpoint of the line connecting them, their combined electric field has a magnitude of 45 N/C.Find the magnitude of the charge.
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To find the magnitude of the charge, we can use Coulomb's Law, which states:
\(F = \frac{{k \cdot q_1 \cdot q_2}}{{r^2}}\)
Where:
- F is the magnitude of the electric force between the charges (given as 45 N/C)
- k is the electrostatic constant (\(9 \times 10^9 \, \text{N m}^2/\text{C}^2\))
- q1 and q2 are the magnitude of the charges we want to find
- r is the distance between the charges (given as 8 cm = 0.08 m)
Since the two charges are of equal magnitude, we can assume \(q_1 = q_2 = q\). Therefore, Coulomb's Law can be rewritten as:
\(F = \frac{{k \cdot q^2}}{{r^2}}\)
We can rearrange the equation to solve for q:
\(q = \sqrt{\frac{{F \cdot r^2}}{{k}}}\)
Now let's substitute the given values into the equation and calculate the magnitude of the charge.