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(where the positive test charge are place at the midpoint)
E=k*3/.01^2 - k*2/.01^2= k/.01^2=100k Nt/coulomb
To calculate the resultant electric field strength at the midpoint between the two charges, you can use the principle of superposition. The electric field due to each charge individually can be calculated using Coulomb's law:
Electric field due to Charge 1 (Q1):
E1 = k * (Q1 / r1^2)
Electric field due to Charge 2 (Q2):
E2 = k * (Q2 / r2^2)
where k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), Q1 and Q2 are the magnitudes of the charges, and r1 and r2 are the distances between the charges and the midpoint, respectively.
In this case, Q1 = +3.0 nC, Q2 = +2.0 nC, r1 = r2 = 2.0 cm (or 0.02 m).
Now, to calculate the resultant electric field, we need to find the vector sum of the individual electric fields at the midpoint. Since the charges have the same sign (+), the electric field vectors will have the same direction.
Resultant electric field (E) = E1 + E2
But since both charges have the same magnitude, E1 = E2. Therefore:
Resultant electric field (E) = 2*E1
Now, let's plug in the values:
E1 = k * (Q1 / r1^2)
E1 = (9.0 x 10^9 N m^2/C^2) * (3.0 x 10^-9 C / (0.02 m)^2)
E1 ≈ 6.75 x 10^5 N/C
Resultant electric field (E) = 2 * E1
E ≈ 2 * (6.75 x 10^5 N/C)
E ≈ 1.35 x 10^6 N/C
So, the resultant electric field strength at the midpoint between the two charges is approximately 1.35 x 10^6 N/C.