Hello. I am having trouble understanding this particular statement found in one of my textbooks.
" Work done to move a charge along a line perpendicular to the field is zero"
The Attempt at a Solution
Field is a space around a charge where if we place any other charge, will result in it experiencing a force.
Field is a 3d space i.e., all the point inside it is able to exert a force on an external charge. And the field lines at a point are just a representation of the force a positive(can it be negative too?) charge experience when placed at that point.
Only an external electric(or due to a magnetic field but that is due to the electric field in turn produced by the magnetic field) field can move a charge inside another electric field. Inorder to do that it must work against the force that keeps the charge in the field. This work changes to potential energy of the charge that got separated from the field.
Now, if the work done is zero that implies there was no electric field/force of attraction which must prevent this motion along that path of motion. It is true that there is no component of a vector along a line perpendicular to a vector(field line). But wouldn't there be other field lines (or their components) in this path i.e., perpendicular to a particular field line, since the field is 3d concept? Or are all field lines aligned in a particular direction?
Kindly correct me if any of the above statements is wrong. Thanks in advance!