Final answer:
The electric field strength 10.0 cm from the wire can be calculated using the equation E = kQ/r^2, where E is the electric field strength, k is the Coulomb constant, Q is the charge, and r is the distance from the wire. By plugging in the given values, we can find that the electric field strength is approximately 1050 N/C.
Step-by-step explanation:
The electric field strength 5.0 cm from a very long charged wire can be calculated using the equation:
E = kQ/r^2
where E is the electric field strength, k is the Coulomb constant (9 x 10^9 Nm²/C²), Q is the charge, and r is the distance from the wire.
Given that the electric field strength at 5.0 cm is 2100 N/C, we can plug in the values and solve for Q:
2100 N/C = (9 x 10^9 Nm²/C²)Q/(0.05 m)²
Solving for Q, we find that Q = 9 x 10^-10 C.
To find the electric field strength 10.0 cm from the wire, we can use the same equation with the known charge:
E = (9 x 10^9 Nm²/C²)(9 x 10^-10 C)/(0.10 m)²
Calculating this, we find that the electric field strength 10.0 cm from the wire is approximately 1050 N/C.