91Ó°ÊÓ

What is the potential difference between $x_i=10cm$ and $x_f=30cm$ in the uniform electric field $E_x=1000V/m$?

Figure Q26.1 shows the $x$-component of $\stackrel{→}{E}$as a function of $x$. Draw a graph of $V\mathrm{versus}x$in this same region of space. Let $V=0V\mathrm{at}x=0m$and include an appropriate vertical scale.

Figure Q26.10 shows a $3V$battery with metal wires attached to each end. What are the potential differences $∆V_{12}=V_2-V_1,∆V_{23}=V_3-V_2,$$∆V_{34}=V_4-V_3,\mathrm{and}∆V_{41}=V_1-V_4$?

Determine the magnitude and direction of the electric field at points 1 and 2 in Figure EX26.10.

Figure EX26.11 is a graph of$V\mathrm{versus}x$. Draw the corresponding graph of$E_x\mathrm{versus}x$.

The parallel-plate capacitor in Figure Q26.11 is connected to a battery having potential difference $∆V_{bat}$. Without breaking any of the connections, insulating handles are used to increase the plate separation to $2d$.

a. Does the potential difference $∆V_C$change as the separation increases? If so, by what factor? If not, why not?

b. Does the capacitance change? If so, by what factor? If not, why not?

c. Does the capacitor charge $Q$change? If so, by what factor? If not, why not?

Figure EX26.12 is a graph of $V\mathrm{versus}x$. Draw the corresponding graph of $E_x\mathrm{versus}x.$

Rank in order, from largest to smallest, the potential differences ${(∆V_C)}_1\mathrm{to}{(∆V_C)}_4$of the four capacitors in Figure Q26.12. Explain.

The electric potential in a region of uniform electric field is$-1000V$ at $x=-1.0m$ and $+1000V\mathrm{at}x=+1.0m$. What is $E_x$?

The electric potential along the $x-axis\mathrm{is}V=100x^2$V, where $x$is in meters. What is $E_x$at

(a) $x=0m$and

(b) $x=1m$?