Work and Voltage Change in Moving a Proton from Infinity to 0.16m

AI Thread Summary
The potential difference for a proton moving from infinity to 0.16 m near a -10 μC charge is -562 kV. The work done by the field is calculated using W = -q * ΔV, resulting in approximately 89.9 x 10^-15 J. Despite the proton being attracted to the negative charge, the work is positive because the force acting on the proton also points toward the negative charge. This indicates that energy is required to move the proton against the electric field. The discussion highlights the importance of understanding the relationship between charge, potential difference, and work in electric fields.
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Homework Statement



Known:

Potential Difference of range 0.16 m < r < infinity is -562 kilovolts
At r = 0.16 there is a -10 μC charge on a conducting sphereQuestion:

How much work would the field do if a proton were moved from infinity to 0.16m? comment on the meaning of the sign.

Homework Equations


W = -ΔU = -q * ΔV
1 e = 1.60 x 10 ^-19 C
1 proton = +1e

The Attempt at a Solution



q = 1.60 x 10 ^-19 C
ΔV = -562 kV
W = -q * ΔV
... = -1.60 x 10 ^-19 C * -562 kV
... = 89.9 x 10 ^-15 J

However, shouldn't a proton wan't to approach a negative charge and thus the work should be negative?
 
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The proton is brought in from infinitely far away to r=0.16 m. It moves toward the negative charge, and the force on it due to the field also points toward the negative charge, so the work should be positive, no?
 
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