Question

The following questions will guide you through some qualitative understanding of finding an electric field if the distribution of electric potential is known. The following picture displays a map of potential difference (vertical axis) for an unknown configuration of charges as a function of x- and y-coordinates (horizontal axes). What is the force experienced by a charged particle placed in the electric field of these charges along A charged particle is placed into an electric field of the charges, whose distribution of the potential difference (shown on the vertical axis) as function of x- and y-coordinates (shown on horizontal axes) is displayed in the picture below. The particle is moving along the trajectory shown by a black curve At which point 1 or 2 along the trajectory does particle experience the t magnitude of the force? impossible to tell the forces will be the same for the same potential difference the forces in an electric field are always the same at any location Explain your reasoning

I just need help with explain your reasoning part

Answer 1

as we can see in the graph that point 1 has a higher potential compared to point 2,as at point 1 we have a higher peak of the graph.

now the force on partical can be given as F=-$\Delta$V

here $\Delta$ is the gradient,and V is the potential

now delta can be defined as rate of change of co-ordinate $\tiny \frac{\partial }{\partial x}$ in x direction only and will have y and z also similarly

so the fast the potential changes with co-ordinate the greater will be the force ;hence at point 1 force it greatest in that case