# Electric field and electric potential problem

The question is from AP Physics C Barron's

Consider the potential-position function shown below(I put it on the attached files)( the potential asymptotically approaches zero as x goes to + infinity or -infinity). The upper limit of the speed that an electron can have as it passes the origin and still remain bound close to the origin is

A. V=√2q(Vmax)/m
B. V=0
C. V=√-2q(Vmax)/m
D. V=2q(Vmax)/m
E. none of the above

Because the charge is negative(electron), the force points away from the origin( rather than toward the origin, as for a positive charge). Therefore. the electron never remains bound close to the origin, but rather always experiences a force away from the origin.

So my confusion is why it says"the force points away from the origin" here, i think according to the formula E= - dV/dx, the B point and D point might the electron been pushed away, but at point C and E, it would be the opposite, since the slope at those two points is positive, the field would be negative, so for electron, wouldn't the force be points toward the origin at point C and E?

#### Attachments

• Untitled.png
37 KB · Views: 401