The Electric Field — Question 6

Question 6

A local field map locates a null by solving simultaneous component conditions

Within a specified small region, $E_x=100-200x$ and $E_y=40+100y$, with coordinates in meters and fields in N/C. There is no z component. The map is taken as exact within the region containing the points used below.

1. Locate the field null and find the field at $(x,y)=(.400,-.300)$ m.

2. Find the force on a $-5.00$ nC probe there. Explain why setting only $E_x=0$ does not identify a field null.

Question 6 - Solution

A local field map locates a null by solving simultaneous component conditions

(a) Method and calculation

$$E_x=0\Rightarrow x=.500\,\mathrm m,\quad E_y=0\Rightarrow y=-.400\,\mathrm m.$$$$\mathbf E(.400,-.300)=(20,10)\,\mathrm{N/C}.$$

(b) Interpretation and further calculation

$$\mathbf F=q\mathbf E=(-100,-50)\,\mathrm{nN}.$$$$|\mathbf E|=0\ \Longleftrightarrow\ E_x=E_y=E_z=0.$$The vertical line $x=.500$ has zero horizontal component but generally a nonzero vertical component.

Physical check

A component zero is coordinate-dependent; a zero vector is not.