Final answer:
To bring a single electron from infinity to Earth, work is done against Earth's electric field of 150 N/C, resulting in work totaling 1.524 x 10^-12 J.
Step-by-step explanation:
To calculate the work required to bring a single electron from infinity to the Earth's surface, we can use the concept of the electric field surrounding the Earth. The Earth is surrounded by a near-uniform electric field approximately 150 N/C, directed downward, which is caused by the ionosphere. The ionosphere, being positively charged, and the Earth, being negatively charged, create this field.
Using the electric field (E) and knowing that the charge of an electron (q) is approximately -1.60 x 10-19 C, the work done (W) is the product of the charge, the electric field, and the distance (d). Since we are interested in bringing the electron from infinity to a distance of 6.371 x 106 m (radius of the Earth), the formula for work done in an electric field is W = qEd. Substituting the given values, the work done in bringing a single electron to the Earth's surface is:
W = (-1.60 x 10-19 C) x (150 N/C) x (6.371 x 106 m)
W = -1.524 x 10-12 joules (J)
Since work is a form of energy, and energy is scalar, we can ignore the negative sign, which indicates direction, for the magnitude of work, which will be 1.524 x 10-12 J.