InterviewSolution
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InterviewSolution
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Uniform electric field of magnitude `100 Vm^-1` in space is directed along the line `y = 3 + x`. Find the potential difference between points `A (3,1) and B (1,3)`. |
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Answer» Equation of the line `y = 3 + x`. The slope of line `tan theta = 1 or theta = 45^(@)` we can express electric field in vector form `vec E = 100 cos theta hat i + 100 sin theta hat j (V m^-1)` Electric field `vec E = |vec E | (cos theta hat i + sin theta hat j)` `vec E = (100)/(sqrt(2)) hat i + (100)/(sqrt(2)) hat j (V m^-1)` `Delta vec r = vec (AB) = vec r_B - vec r _A = (hat i + 3 hat j)-(3 hat i + hat j)= -2 hat i + 2 hat j` `Delta V = - vec E . Delta vec r = - ((100)/(sqrt(2)) hat i + (100)/(sqrt(2)) hat j). Delta vec r` = `- ((100)/(sqrt(2)) hat i + (100)/(sqrt(2)) hat j) . (-2 hat i + 2 hat j)` =`-100 sqrt(2) + 100 sqrt(2)` `V_A - V_B = 0`. |
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