Question

what is potential energy gradient? and why is force the negative of potential energy gradient?

Answer 1

Dear student,

Potential energy gradient is rate of change of potential energy with respect of displacement.
The force and displacement define work done.Work done combined with conservation of energy dictate loss of potential energy.The minus sign is because the work done on the object by the force must be equal to loss of potential energy due to the displacement of that object in field.
$Force=-\frac{∆U}{∆x}$

Regards.