An electric field in a certain region of space is given by E = (10x i + 20y j ) V/m , where x and y are in meters. If the electric potential at the origin is 10 V , the electric potential at the point (2 m , 1 m ) is :

Step-by-step solution

The relationship between electric potential and electric field is given by dV = - E d r . Here, d r = dx i + dy j . dV = -(10x i + 20y j ) (dx i + dy j ) = -10x dx - 20y dy Integrating both sides from the origin (0,0) to the point (2,1) : ₁₀^ V dV = - ₀² 10x dx - ₀¹ 20y dy V - 10 = - [ 10x^2 2 ]₀² - [ 20y^2 2 ]₀¹ V - 10 = -5(2^2 - 0) - 10(1^2 - 0) V - 10 = -20 - 10 = -30 V = 10 - 30 = -20 V Thus, the electric potential at the point (2, 1) is -20 V . Answer: -20 V