Question

Points A at (3,6) meters and B at (8, -3) meters are in a region where the electric field is uniform and given by E= 12i N/C, What is the electric potentialdifference V_A-V_B?

The answer is -60 V, what is the procedure to this answer

Answer 1

Given that the postion of the point \(A=3 i+6 j\)

The postion of the point \(B=8 i-3 j\)

Electric filed \(E=12 i\)

The position vector is \(r=B-A\)

$$ \begin{array}{l} =(8 i-3 j)-(3 i+6 j) \\ =(5 i-9 j) \end{array} $$

The potential difference between points \(A\) and \(B\) is

$$ \begin{aligned} V_{A B} &=-E \cdot d r \\ V_{A B} &=-(12 i) \cdot(5 i-9 j) \\ V_{A B} &=-((12 \times 15) i . i-(12 \times 9) i . j) \\ V_{A B} &=-(60-0) \quad(\text { Since } i . i=1 \text { and } i . j=0) \\ V_{A B} &=-60 \mathrm{~V} \end{aligned} $$