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Chapter 32: Q13P (page 967)

At what rate must the potential difference between the plates of a parallel-plate capacitor with a $2.0 渭 F$ capacitance be changed to produce a displacement current of $1.5 A$ ?

Short Answer

Expert verified

The rate of potential is $7.5 脳 10^{5} V/s$ .

Step by step solution

01

Given data

$C = 2.0 渭 F$

$i_{d} = 1.5 A$

02

Determining the concept

By using the concept of displacement current and by using equation 32-10, write the equation for flux as a function of potential, and from that, find the rate of change of potential difference. The rate of change of potential difference across the plates of the capacitor is displacement current per unit capacitance.

Formulae are as follows:

$i_{d} = 蔚_{0} \frac{d 蠒_{E}}{d t}$

where, 'i' is current, $蠒$ is the flux.

03

Determining the rate of change of potential difference

From the equation 32-10,

$i_{d} = 蔚_{0} \frac{d 蠒_{E}}{d t}$

Where, $蠒 = A E$ theand the $E = \frac{V}{d}$ .

So,

$蠒_{E} = \frac{A V}{d}$

So,

$i_{d} = \frac{A 蔚_{0}}{d} \frac{d V}{d t}$

Where, the capacitance,

$C = \frac{A 蔚_{0}}{d}$

So, the rate of potential is,

$\frac{d V}{d t} = \frac{i_{d}}{C} \frac{d V}{d t} = \frac{1.5}{2.0 脳 10^{- 6}} \frac{d V}{d t} = 7.5 脳 10^{5} V/s$

Hence, the rate of potential is $7.5 脳 10^{5} V / s$ .

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Most popular questions from this chapter

The figure 32-30 shows a circular region of radius $R = 3.00 cm$ in which a displacement current is directed out of the page. The displacement current has a uniform density of magnitude (a) What is the magnitude of the magnetic field due to displacement current at a radial distance 2.00 cm ?(b) What is the magnitude of the magnetic field due to displacement current at a radial distance 5.00 cm?

Replace the current loops of Question 8 and Fig. 32-24 with paramagnetic spheres. For each field, are (a) the magnetic dipole moment of the sphere and (b) the magnetic force on the sphere directed up, directed down, or zero?

Figure 32-23 shows a face-on view of one of the two square plates of a parallel-plate capacitor, as well as four loops that are located between the plates. The capacitor is being discharged. (a) Neglecting fringing of the magnetic field, rank the loops according to the magnitude of $鈭� \overset{鈬赌}{B} 路 d \overset{鈬赌}{s}$ along them, greatest first. (b) Along which loop, if any, is the angle between the directions of $\overset{鈬赌}{B} a n d d \overset{鈬赌}{s}$ constant (so that their dot product can easily be evaluated)? (c) Along which loop, if any, is B constant (so that B can be brought in front of the integral sign in Eq. 32-3)?

The magnetic flux through each of five faces of a die (singular of 鈥渄ice鈥�) is given by $蠁_{B} = 卤 N W b$ , where N(= 1 to 5) is the number of spots on the face. The flux is positive (outward) for Neven and negative (inward) for Nodd. What is the flux through the sixth face of the die?

Two plates (as in Fig. 32-7) are being discharged by a constant current. Each plate has a radius of $4.00 cm$ . During the discharging, at a point between the plates at radial distance $2.00 cm$ from the central axis, the magnetic field has a magnitude of $12.5 nT$ . (a) What is the magnitude of the magnetic field at radial distance $6.00$ ? (b) What is the current in the wires attached to the plates?

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