Apiece of wire is bent to form a circle with radius r. it has a steady current i flowing through it in a counterclockwise direction as seen from the top (looking in the negative z-direction).
what is bz(0), the z component of b at the center (i. e., x=y=z=0) of the loop?
express your answer in terms of i, r, and constants like μ0 and π.

B=μ₀I/2r

Explanation:

Produced magnetic field due to an existing electric field through a coil or conductor can be explained by Biot-Savart Law. Formula for this law is:

dB=(μ₀I/4π.r²)dL

Here,

r=Radius of the loop

I and r are constants with respect to length L.

To convert linear displacement L into angular displacement Ф:

dL=r.dФ

So,

dB=(μ₀I/4π.r²)r.dФ

dB=(μ₀I/4π.r)dФ

Integrating both sides over the circle i.e. from 0 radians to 2π radians  (360⁰), while the integration will apply only on dФ as all others are constants.

B=(μ₀I/4πr)(2π-0)

B=(μ₀I/2r)

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s