Physics, 06.05.2020 06:36 homework1911

A time-dependent but otherwise uniform magnetic field of magnitude Bo(t) is confined in a cylindrical region of radius 6.5 cm. Initially the magnetic field in the region is pointed out of the page and has a magnitude of 3.5 T, but it is decreasing at a rate of 29.5 G/s. Due to the changing magnetic field, an electric field will be induced in this space which causes the acceleration of charges in the region.

Required:
What is the direction of acceleration of a proton placed in at the point 1.5 cm from the center?

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Answer from: rosebelll4555

The acceleration is a = 9197.11 m/s^2

Explanation:

From the question we are told that

The radius of the cylinder is $r = 6.5 \ cm = \frac{6.5}{100} = 0.065 m$

The magnitude of the magnetic field is B_i = 3.5T

The rate of decrease is $\frac{dB}{dt} = 29.5 \ G/s = \frac{29.5}{10000} = 29.5 * 10 ^{-4} T/s$

The distance from the center is $D = 1.5\ cm = \frac{1.5}{10}=0.15m$

Faraday's law of induction states mathematically that

$\epsilon = \frac{d \o}{dt}$

$\epsilon = \int\limits {E} \, dl$

Where $\epsilon$ is the induced emf

E is the magnitude of the electric field

i the change in length

$d \o$ is the change in magnetic flux which is mathematically represented as

$\o = BA$

substituting this into the above equation

$\int\limits {E} \, dl = \frac{d(BA)}{dt }$

$E l = A \frac{dB}{dt}$

Where l is the circumference of the circular loop formed in the cylinder which is mathematically represented as

$l = 2\pi r$

And A is the area of the circular loop formed which is mathematically represented as

$A = \pi r^2$

$E (2 \pi r ) = (\pi r^2 ) \frac{dB}{dt}$

$E = \frac{r}{2} \frac{dB}{dt}$

Substituting value

$E = \frac{0.065}{2} * 29.5 *10^{-4}$

$= 9.588*10^{-5} \ V/m$

Generally acceleration is mathematically represented as

$a = \frac{F}{m}$

Now F is the electric force which is mathematically represented as

F = qE

Substituting this into the question

$a = \frac{qE }{m }$

Where q is the charge on the proton with a constant value of

$q = 1.60 *10^ {-19 } C$

and m is the mass of the proton with a constant value of

$m = 1.67 *10^{-31} kg$

Substituting values

$a = \frac{1.60*10^{-19} * 9.588 *10^{-5}}{1.67 *10^{-27}}$

a = 9197.11 m/s^2

Answer from: Quest

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

Answer from: Quest

the best answer for these questions would be:

1. c. is smaller

2. d) concrete operational

3. b) interaction with the environment – the children interact with their environment can them learn more.

4. a) parents who reason openly with children can limit a child’s cognitive ability.

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