Final answer:
A point charge with a magnitude of 5 x 10^-6 C creates a 10,000 N/C electric field at a distance of 0.250 m. The electric field at a distance of 10.0 m is 4.5 x 10^7 N/C.
Step-by-step explanation:
To find the magnitude of a point charge that creates a 10,000 N/C electric field at a distance of 0.250 m, we can use the formula for electric field:
E = k * q / r^2
where E is the electric field, k is Coulomb's constant (approximately 9 x 10^9 N m^2/C^2), q is the magnitude of the point charge, and r is the distance from the point charge.
Rearranging the formula, we get:
q = E * r^2 / k
Substituting the given values, we have:
q = (10,000 N/C) * (0.250 m)^2 / (9 x 10^9 N m^2/C^2)
q = 5 x 10^-6 C
Therefore, a point charge with a magnitude of 5 x 10^-6 C creates a 10,000 N/C electric field at a distance of 0.250 m.
For part (b), to find the magnitude of the electric field at a distance of 10.0 m, we can use the same formula:
E = k * q / r^2
Substituting the values, we have:
E = (9 x 10^9 N m^2/C^2) * (5 x 10^-6 C) / (10.0 m)^2
E = 4.5 x 10^7 N/C
Therefore, the electric field at a distance of 10.0 m is 4.5 x 10^7 N/C.