1) Potential difference: 144.6 V
2) Potential difference: -909 V
Explanation:
1)
Given an electric field in three dimensions, with components , we have that each component of the field is related to the electric potential V by:
For the field in this problem, we know that
Which means that
and so the potential does not depend on z, so we can re-write it as .
Then we take the equation in x:
Solving for V,
where f(y) is a function depending on y.
From the equation in y,
And substituting the expression of V,
We know also that
And by comparing these last 2 equations, we infer that
So, the expression for the electric potential is
where C is a constant.
Now we can find the electrical potential difference between the origin and the other point.
The origin has coordinates (0,0,0), so the potential is
(V)
The other point has coordinates (-2.7 m,4.1 m,0.0 m), so the potential is
(V)
So, the potential difference is
2)
In this second case, we want to find the potential difference between the origin and another point.
The potential is
The origin has coordinates (0,0,0), so the potential is
(V)
The second point has coordinates (4.2 m, 5.9 m, 0.0 m), so the potential there is
(V)
Therefore, the potential difference is given by the difference of these two values:
Learn more about electric field and potential:
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