A metal sphere of radius R = 28 cm carries a total charge Q = 0.5 microC. What is the magnitude of the electric field (in N/C) just outside the sphere?
To find the magnitude of the electric field just outside the sphere, we can use the formula for electric field due to a charged sphere. The formula is:
E = k * Q / r²
where E is the electric field, k is the Coulomb's constant (8.99 × 10^9 N m²/C²), Q is the total charge on the sphere, and r is the distance from the center of the sphere.
In this case, the radius of the sphere is given as R = 28 cm. The charge on the sphere is given as Q = 0.5 microC (0.5 × 10^-6 C).
To find the electric field just outside the sphere, we need to consider the distance from the center of the sphere to a point just outside the surface. Since the sphere has a radius of R, the distance from the center to just outside the surface is R + small distance.
Assuming that the small distance is negligible compared to the radius, we can say that the distance is approximately equal to the radius.
Therefore, the distance (r) from the center of the sphere to the point just outside the surface is R.
Plugging in the values into the formula, we have:
E = (8.99 × 10^9 N m²/C²) * (0.5 × 10^-6 C) / (28 cm)²
First, let's convert the radius to meters:
R = 28 cm = 0.28 m
Now, let's calculate the expression:
E = (8.99 × 10^9 N m²/C²) * (0.5 × 10^-6 C) / (0.28 m)²
E = (8.99 × 0.5 × 10^3 N m²/C) / (0.0784 m²)
E = 5.6475 × 10^6 N/C
Therefore, the magnitude of the electric field just outside the sphere is approximately 5.6475 × 10^6 N/C.