Physics, 01.07.2020 16:01, victoria6929

Suppose that a circular parallel-plate capacitor has radius R0 = 3.0 cm and plate separation d = 5.0 mm. A sinusoidal potential difference V = V0 sin(2πft) is applied across the plates, where V0 = 150 V and f = 60 Hz. In the region between the plates, find the magnitude of the induced magnetic field versus R and t, where R is the radial distance from the capacitor’s central axis. Assume that B = B0(R) is the amplitude of the magnetic field.

Answers: 3

Show answers

Answers

answered: anthony1366

$B=\frac{\mu_o \epsilon_o R_o^2V_o}{2rd}cos(\omega t)$

Explanation:

By the information of the statement you have that the sinusoidal potential difference is given by:

$V=V_osin(\omega t)=V_osin(2\pi ft)=150sin(2\pi (60)t)$ (1)

In order to calculate the induced magnetic field in between the plates, you first take into account the following formula, which is the Ampere-Maxwell law:

$\int B\cdot ds=\mu_o \epsilon_o\frac{d\Phi_E}{dt}+\mu_oI_c$ (2)

B: induced magnetic field

μo: magnetic permeability of vacuum = 4π*10^-7 A/T

εo: dielectric permittivity of vacuum = 8.85*10^-12 C^2/Nm^2

Ic: conduction current

ФE: electric flux

There is no conduction current in between the plates, then Ic = 0A

Next, you calculate dФE/dt, as follow:

The electric field, and the electric flux, are:

$E=\frac{V}{d}=\frac{V_osin(\omega t)}{d}\\\\\Phi_E=EA$

d: separation between plates = 5.0mm = 5.0*10^-3 m

A: area of the circular plates = $\pi R_o^2$

Ro: radius of the circular capacitor = 3.0cm = 0.03m

Thus, dФE/dt is:

$\frac{d\Phi_E}{dt}=\frac{d(EA)}{dt}=\pi R_o^2\frac{d}{dt}[\frac{V_osin(\omega t)}{d}]\\\\\frac{d\Phi_E}{dt}=\frac{\pi \omega R_o^2 V_o}{d}cos(\omega t)$ (3)

The induced magnetic field is calculated by taking into account that the integral of the equation (2) is:

$\int B \cdot ds=B\int ds=B(2\pi r)$ (4)

Next, you replace the results of (3) and (4) into the equation (2) and you solve for B:

$B(2\pi r)=\mu_o \epsilon_o (\frac{\pi \omega R_o^2 V_o}{d}cos(\omega t))\\\\B=\frac{\mu_o \epsilon_o R_o^2V_o}{2rd}cos(\omega t)$ (5)

The last expression is de induced magnetic field in between the plates in terms of t and r

Another way of expressing the formula (5) is as follow:

$B=B_ocos(\omega t)\\\\B_o=\frac{\mu_o \epsilon_o R_o^2V_o}{2rd}$

answered: Guest

answer and explanation;

composition refers to both the types of minerals within a rock and the overall chemical makeup of the rock while texture refers to the size and arrangement of the minerals or grains that make up a rock. both composition and texture can be used to classify rocks, such as igneous rocks. texture describes how the rock became solid or crystallized from liquid, melted rock. composition of a rock describes the minerals that make up a particular rock.

answered: Guest

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

hope this ! this is not copied! search it up, it's free of plagiarism!

Other questions on the subject: Physics

Physics, 21.06.2019 21:10, Ashley606hernandez

Tafari worked one summer on a ship that set weather buoys in the ocean. he watched how one of the buoys moved in the water. describe which parts of the wave would cause the buoy to bob up and down. which wave property determined how fast the buoys bobbed in the water? he observed that when the wind blew harder, the ocean waves were larger, and the buoys moved away from the ship. what effect, if any, did the waves have on how far the buoys moved? explain your answer.

Answers: 3

continue

Physics, 21.06.2019 23:30, reggiegilbert1995

Which simple machine is not part of this compound machine? a. lever b. pulley c. inclined plane d. wheel and axle

Answers: 1

continue

Physics, 23.06.2019 16:00, siri5645

In an exothermic chemical reaction the energy gained by the surroundings must be the energy lost by the reaction

Answers: 3

continue

Physics, 23.06.2019 19:00, coollid876

Determine which heat transfers below are due to the process of conduction. i) you walk barefoot on the hot street and it burns your toes. ii) when you get into a car with hot black leather in the middle of the summer and your skin starts to get burned. iii) a flame heats the air inside a hot air balloon and the balloon rises. iv) a boy sits to the side of a campfire. he is 10 feet away, but still feels warm. a) i and ii b) iii and iv c) i, ii, and iv d) ii, iii, and iv

Answers: 1

continue

Do you know the correct answer?

Suppose that a circular parallel-plate capacitor has radius R0 = 3.0 cm and plate separation d = 5.0...