Answer:
a) 5.28 * 10^6 C
b) -3.04× 10^-20 N
Step-by-step explanation:
a) To calculate the value of the charge, we can use Coulomb's Law, which states that the electric force between two charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, we know the electric field strength E and the distance r, and we can use the equation:
E = k * Q / r^2
where k is Coulomb's constant (9 × 10^9 N·m^2/C^2), Q is the value of the charge, and r is the distance. Solving for Q, we get:
Q = E * r^2 / k
Substituting the given values, we get:
Q = 190,000 N/C * (0.5 m)^2 / (9 × 10^9 N·m^2/C^2)
Q ≈ 5.28 * 10^6 C
Therefore, the value of the charge is approximately 5.28 * 10^6 C.
b) To calculate the force on an electron at that location, we can use Coulomb's Law again. The force F between two charges is given by:
F = k * q1 * q2 / r^2
where q1 and q2 are the charges and r is the distance between them. In this case, the electron has a charge of -1.6 × 10^-19 C (negative because it is an electron) and is located 0.5 m away from the initial charge. So the force on the electron is:
F = k * Q * (-1.6 × 10^-19 C) / (0.5 m)^2
F = (9 × 10^9 N·m^2/C^2) * (5.28 × 10^-12 C) * (-1.6 × 10^-19 C) / (0.5 m)^2
F ≈ -3.04× 10^-20 N
The negative sign indicates that the force is attractive, meaning that the electron would be pulled towards the unknown charge.