When an electron moves from A to B along an electric field line, the electric field does 3.94 x 10^-19 J of work on it. What are the electric potential differences (a) Vb - Va, (b) Vc - Va, and (c) Vc - Vb?
To determine the electric potential differences, you need to use the relationship between work done by an electric field and the change in electric potential (V). The work done by the electric field on an electron can be calculated using the equation:
Work (W) = q * ΔV
Where:
- W is the work done by the electric field on the electron (given as 3.94 x 10^-19 J).
- q is the charge of the electron (q = -e, with e being the elementary charge of an electron, approximately equal to 1.6 x 10^-19 C).
- ΔV is the change in electric potential.
Now we can calculate the electric potential differences.
(a) Vb - Va:
Since Work (W) = q * ΔV, we can rearrange the equation as follows:
ΔV = W / q
Plugging in the given values:
ΔV = 3.94 x 10^-19 J / (-1.6 x 10^-19 C)
Calculating:
ΔV = -2.46 V
Therefore, Vb - Va = -2.46 V.
(b) Vc - Va:
To calculate Vc - Va, we need to add the potential difference from B to C (ΔVbc) with the potential difference from A to B (ΔVab).
Since ΔVab = -2.46 V (as calculated in (a)), and the potential difference ΔVbc is not given, we cannot determine Vc - Va without more information.
(c) Vc - Vb:
Similarly, to calculate Vc - Vb, we need to subtract the potential difference from A to B (ΔVab) from the potential difference from A to C (ΔVac).
Again, since ΔVab = -2.46 V (as calculated in (a)), and the potential difference ΔVac is not given, we cannot determine Vc - Vb without more information.