Two point charges of magnitude +3.0 nC and +2.0 nC respectively are placed 2.0cm apart. Calculate the resultant electric field strength at their midpont
E= E1 + E2
E=k(3/d^2 +2/d^2) where d is the half distance
E=k(5/d^2) now d=.01m so
E=k(5E-4) N/C
To calculate the resultant electric field strength at the midpoint of two point charges, you need to determine the individual electric field strengths produced by each charge and then add them together.
The formula for the electric field strength produced by a point charge is given by:
E = k * (Q / r^2)
Where:
- E is the electric field strength
- k is Coulomb's constant (k = 9 × 10^9 N m²/C²)
- Q is the magnitude of the point charge
- r is the distance from the point charge to the location where you want to find the electric field strength
Let's calculate the electric field strengths produced by each point charge separately:
For the first charge (Q1 = +3.0 nC):
Using the given distance of 2.0 cm = 0.02 m, we have:
r1 = 0.02 m
E1 = k * (Q1 / r1^2)
Substituting the values:
E1 = (9 × 10^9 N m²/C²) * (3.0 × 10^(-9) C) / (0.02 m)^2
Simplifying the equation further:
E1 = (9 × 10^9 N m²/C²) * (3.0 × 10^(-9) C) / (0.0004 m)
Calculating E1:
E1 = 6.75 × 10^4 N/C
For the second charge (Q2 = +2.0 nC):
Using the same distance of 2.0 cm = 0.02 m as before, we have:
r2 = 0.02 m
E2 = k * (Q2 / r2^2)
Substituting the values:
E2 = (9 × 10^9 N m²/C²) * (2.0 × 10^(-9) C) / (0.02 m)^2
Simplifying the equation further:
E2 = (9 × 10^9 N m²/C²) * (2.0 × 10^(-9) C) / (0.0004 m)
Calculating E2:
E2 = 4.5 × 10^4 N/C
Now that we have calculated the electric field strengths produced by each charge, we can find the resultant electric field strength at their midpoint by summing them:
E = E1 + E2
Substituting the values we obtained earlier:
E = 6.75 × 10^4 N/C + 4.5 × 10^4 N/C
Calculating the sum:
E = 11.25 × 10^4 N/C
Therefore, the resultant electric field strength at the midpoint of the two point charges is 11.25 × 10^4 N/C.