1. Two concentric conducting spherical shells have radii of 0.145 m. and 0.215 m. The inner sphere bears a charge of -3.00E-08 C. An electron escapes from the inner sphere with negligible speed. Assuming that the region between the spheres is a vacuum, compute the speed (in meters/second) with which the electron strikes the outer sphere.
is this possible as there is no electric field inside of a conductor?
Did no one answer this question?
What an awful website haha, I haven't found a single answered question here
Yes, you are correct that there is no electric field inside a conductor in electrostatic equilibrium. However, in this case, the electron is escaping from the inner sphere, so it is initially outside the conductor.
To solve this problem, we need to find the potential difference between the inner and outer spheres and use that to calculate the electron's speed when it strikes the outer sphere. Here are the steps:
1. Find the potential difference between the inner and outer spheres using the formula:
ΔV = k * (Q / r_inner - Q / r_outer)
where k is the electrostatic constant (9.0 × 10^9 Nm^2/C^2), Q is the charge on the inner sphere (-3.00E-08 C), r_inner is the radius of the inner sphere (0.145 m), and r_outer is the radius of the outer sphere (0.215 m).
2. Once you have the potential difference, you can use the conservation of energy to find the speed of the electron. The potential energy lost by the electron as it moves from the inner sphere to the outer sphere is converted into its kinetic energy. Therefore,
ΔPE = ΔKE
q * ΔV = 1/2 * m * v^2
where q is the charge of the electron (-1.6 × 10^-19 C), ΔV is the potential difference, m is the mass of the electron (9.11 × 10^-31 kg), and v is the speed of the electron.
3. Rearrange the equation and solve for v:
v = √(2 * q * ΔV / m)
4. Substitute the values for q, ΔV, and m into the equation and solve for v.