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- Homework Statement
- Hello, I have a question asking me to draw a radial gravitational field showing the gravitational field lines and the equipotential surfaces for equal energy increments. I then have to comment upon the spacing of the field lines and equipotential lines.

My query is in this question would it be referring to the spacing visually when drawing the field lines and equipotentials or what this spacing represents in a radial field?

I am not sure how to comprehensively answer what is being asked and would be very grateful for any advice

- Relevant Equations
- g=GM/r^2

I have just attached a standard depiction of a radial field as one may similarly choose to draw it. So I understand that the gravitational field strength in a field is defined as the force per unit mass at that point. The field lines in a radial field move further apart further away from the centre indicating the field strength is reducing. The closer together the field lines the stronger the field and thus the force.

The equipotential surfaces of a radial field are positions within a field with zero difference in potential between them; ie. the potential on an equipotential surface is the same everywhere as connected by equipotential lines. The field will always be perpendicular to the equipotential lines; since a field is defined as a region in which potential changes. How close the equipotentials are indicates the strength of the electric field and how quickly the potential is changing. e.g. a stronger field has closer equipotentials.

In a radial field, the field lines are all equally separated in terms of field strength but the radial distance between them increases as you move further from the planet. If this question is just asking how to draw a general radial field with field and equipotential lines then one would say that the field lines are evenly spaced but increase in distance further from the centre? And moreover, would the equipotential surfaces be said

So for a radial field the field lines are evenly spaced but the equipotential surfaces are unevenly spaced?

Moreover, could an alternative unit for gravitational field strength besides N kg^-1 be Jm^-1kg^-1?

The equipotential surfaces of a radial field are positions within a field with zero difference in potential between them; ie. the potential on an equipotential surface is the same everywhere as connected by equipotential lines. The field will always be perpendicular to the equipotential lines; since a field is defined as a region in which potential changes. How close the equipotentials are indicates the strength of the electric field and how quickly the potential is changing. e.g. a stronger field has closer equipotentials.

In a radial field, the field lines are all equally separated in terms of field strength but the radial distance between them increases as you move further from the planet. If this question is just asking how to draw a general radial field with field and equipotential lines then one would say that the field lines are evenly spaced but increase in distance further from the centre? And moreover, would the equipotential surfaces be said

**visually**to be**drawn**unequally spaced with successive shells representing equal intervals of potential difference.So for a radial field the field lines are evenly spaced but the equipotential surfaces are unevenly spaced?

Moreover, could an alternative unit for gravitational field strength besides N kg^-1 be Jm^-1kg^-1?