A particle of mass 2 g and charge 10 C is projected from the origin with a speed of 5 m/s . The region has a non-uniform electric field given by E = -100(y i + x j ) V/m , where x and y are in meters. The speed of the particle when it reaches the point (3, 4) m is

Step-by-step solution

The relation between electric field and potential is dV = - E d r . Substituting the given electric field: dV = -[-100(y i + x j )] (dx i + dy j ) dV = 100(y dx + x dy) Recognizing the perfect differential d(xy) = y dx + x dy , we get: dV = 100 d(xy) Integrating from the origin (0,0) to the point (3,4) : V = V(3,4) - V(0,0) = 100 [xy]_ (0,0) ^ (3,4) V = 100(3 4 - 0) = 1200 V The change in potential energy of the particle is: U = q V = (10 10⁻⁶ C )(1200 V ) = 0.012 J According to the work-energy theorem, the work do