Question

For each function, determine whether its gradient points radially outward from the origin, radially inward toward the origin, radially outward from the z-axis, or radially inward toward the z-axis?

1) Radially outward from the origin
2) Radially inward toward the origin
3) Radially outward from the z-axis
4) Radially inward toward the z-axis

Answer 1

In physics, the direction of the gradient can be determined by considering the forces or velocities involved. It can point radially outward or inward from the origin or the z-axis.

Step-by-step explanation:

In physics, the direction of the gradient can be determined by considering the forces or velocities involved. For example:

1. Radially outward from the origin: This means that the gradient points away from the center of the coordinate system, like in the case of a radial electric field pointing away from a positive charge at the origin.
2. Radially inward toward the origin: This means that the gradient points towards the center of the coordinate system, like in the case of a radial electric field pointing towards a negative charge at the origin.
3. Radially outward from the z-axis: This means that the gradient points away from the z-axis, like in the case of the electric field between two conductors with a common axis.
4. Radially inward toward the z-axis: This means that the gradient points towards the z-axis, like in the case of the electric field between two opposite charges on the z-axis.