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Consider a space with a constant electric field pointing up E = Ek, with E =1 (in units
of V/m). Consider a point P, with coordinates (expressed in metres) r1 = (1,3, 3) and
electric potential V1, and a point P, with coordinates r2 = (3,0, 4) and potential V2.
Then the potential difference V, – Vị is given by how many volts (and mind the sign)?

Expert Solution

Step 1

$G i v e n : E = 1 \hat{k} V / m, r_{1} = (1, 3, 3), r_{2} = (3, 0, 4)$

The electric field in a region is defined by the negative of the gradient of the potential.

As the electric field is along the z-axis, the gradient of the potential has to be found along the z-axis.

Thus, we can write :

$E = - \frac{d V}{d z} E = - \frac{V_{2} - V_{1}}{z_{2} - z_{1}}$

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