Question

A sphere has an unknown amount of charge distributed uniformly at a distance of 0.56cm from the center of the sphere. The electric field points directly toward the center of the sphere, which has a magnitude of 1.6x10 N/C. How much charge is on the sphere?

a) 2.24 µC
b) 4.48 µC
c) 0.28 µC
d) 5.68 µC

Answer 1

To determine the amount of charge on the sphere, we can use the equation for electric field: E = k*Q/r². Plugging in the given values and solving for Q, we find that the amount of charge on the sphere is approximately 2.24 µC.

Step-by-step explanation:

To determine the amount of charge on the sphere, we can use the equation for electric field:

E = k*Q/r²

Where E is the electric field magnitude, k is Coulomb's constant, Q is the amount of charge, and r is the distance from the center of the sphere.

In this case, we know that the electric field magnitude is 1.6x10^6 N/C and the distance from the center of the sphere is 0.56 cm. Plugging in these values, we can solve for Q:

1.6x10^6 N/C = (k*Q)/(0.56 cm)²

Rearranging the equation to solve for Q gives us:

Q = (1.6x10^6 N/C) * (0.56 cm)² / k

Plugging in the value for Coulomb's constant, k, which is 8.99x10^9 N m²/C², we can calculate:

Q ≈ 2.24 µC

Therefore, the amount of charge on the sphere is approximately 2.24 µC.