A solid sphere of radius 49 cm has a total positive charge of 27 µC uniformly di

Question

A solid sphere of radius 49 cm has a total positive charge of 27 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at 120 cm from the center of the sphere.

E =   ___________________ N/C

Figure 24.10 The point charge q is at the center of the spherical gaussian surface, and is parallel to d at every point on the surface.

A single charge is the simplest possible charge distribution, and we will use this familiar example to show the technique of solving for the electric field with Gauss' law. We choose a spherical gaussian surface of radius rcentered on the point charge as in Figure 24.10.

The electric field of a positive point charge is directed radially outward by symmetry and is therefore normal to the surface at every point. As in condition 2, is therefore parallel to d at each point on the surface, so · d= E dA and Gauss' law gives the following.

By symmetry, E is constant everywhere on the surface, which satisfies condition 1, and so it can be removed from the integral. Therefore, we have the following expression where we have used that the surface area of a sphere is 4r2.

We now solve for the electric field which is the familiar electric field of a point charge that we developed from Coulomb's law. (Use the following as necessary: ke, q, and r.)

= ________________

A solid sphere of radius 49 cm has a total positive charge of 27 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at 120 cm from the center of the sphere.

E =   ___________________ N/C

Caussian surface

Explanation / Answer

When a point is away from the sphere, The formula used is

E = kq/r^2

here, the radius of the sphere is redundant if the total charge is already known. R = 120cm = 1.2m

E = 9 x 10^9 x 27 x 10^-6 / 1.2^2 = 168750 N/C

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