1. Two concentric conducting spherical shells have radii of 0.126 m. and 0.225 m. The inner sphere bears a charge of -8.00E-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.

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To compute the speed with which the electron strikes the outer sphere, we can use the principles of electrostatics and conservation of energy.

First, let's calculate the potential difference between the inner and outer spheres. The potential difference (ΔV) is given by the equation:

ΔV = (Q / 4πε₀) * (1 / r₂ - 1 / r₁)

Where:
- Q is the charge on the inner sphere (-8.00E-08 C),
- ε₀ is the permittivity of free space (8.85E-12 C²/N m²),
- r₁ is the radius of the inner sphere (0.126 m), and
- r₂ is the radius of the outer sphere (0.225 m).

Plugging in the values, we have:

ΔV = (-8.00E-08 C / 4π * 8.85E-12 C²/N m²) * (1 / 0.225 m - 1 / 0.126 m)

Next, we know that the electric potential difference is equal to the change in electrical potential energy per unit charge, or:

ΔV = ΔPE / q

Where:
- ΔPE is the change in potential energy,
- ΔV is the potential difference,
- q is the charge of the electron (1.60E-19 C).

Rearranging the equation, we have:

ΔPE = ΔV * q

Now, we know that the change in kinetic energy (ΔKE) of the electron is equal to the change in potential energy. Therefore:

ΔKE = ΔPE

Since the electron escapes from the inner sphere with negligible speed, we can consider its initial kinetic energy to be zero.

Therefore:

KE_final = KE_initial + ΔKE
KE_final = 0 + ΔKE
KE_final = ΔKE

The final kinetic energy of the electron is given by:

KE_final = (1/2) * m * v²

Where:
- m is the mass of the electron (9.11E-31 kg),
- v is the speed of the electron.

Equating the final kinetic energy to the change in kinetic energy, we obtain:

(1/2) * m * v² = ΔKE

Simplifying the equation, we can solve for v:

v = √(2 * ΔKE / m)

Now, we can substitute the value of ΔKE with the value of ΔV * q:

v = √(2 * ΔV * q / m)

Plugging in the values, we can now calculate v.