A thin metallic spherical shell of radius $50 \mathrm{~cm}$ has a total charge of $4.0 \mu \mathrm{C}$ placed on it. At the center of the shell is placed a point charge of $2.00 \mu \mathrm{C}$. What is the electric field at a distance of $90 \mathrm{~cm}$ from the center of the spherical shell?

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Quizplus · Accepted Answer

The electric field at a distance of $90 \mathrm{~cm}$ from the center of the spherical shell can be calculated using the formula for the electric field due to a point charge, $E = \frac{kQ}{r^2}$, where $k$ is Coulomb's constant ($9 \times 10^9 \mathrm{~N m^2/C^2}$), $Q$ is the total charge (the sum of the charge on the shell and the point charge at the center, $4.0 \mu \mathrm{C} + 2.0 \mu \mathrm{C} = 6.0 \mu \mathrm{C}$), and $r$ is the distance from the center ($90 \mathrm{~cm} = 0.9 \mathrm{~m}$). Plugging in the values, $E = \frac{(9 \times 10^9)(6.0 \times 10^{-6})}{(0.9)^2}$, results in an electric field of $6.7 \times 10^{4} \mathrm{~N} / \mathrm{C}$ outward, since the electric field lines due to a positive charge radiate outward.

A Thin Metallic Spherical Shell of Radius 50 cm50 \mathrm{~cm}50 cm Has a Total Charge Of

A Thin Metallic Spherical Shell of Radius $50 \mathrm{~cm}$ Has a Total Charge Of