At a particular instant, a proton is traveling horizontally with a velocity of 531 km/s directed to the east through a region of uniform magnetic field that is directed vertically upward and has a magnitude of 21.5 mT. What is the radius of the circular path along which the proton is traveling

Explanation:

Given a proton, a proton is a positively charge particle,

q=1.609×10^-19C

The mass of proton is given as

M=1.67×10^-27kg

Velocity of the proton is

V=531km/s

Since 1km=1000m

Then, V=531,000m/s

From the Cardinal point eastward is negative direction of x

The proton is then directed eastward

Then, v=-531,000 i m/s

Magnetic field is given as

B=21.5mT

B=21.5×10^-3T

Magnetic field is directed upward i.e positive direction of y axis

Then,

B=21.5 j mT

This shows that the angle between the magnetic field and the velocity is θ=90°. They are perpendicular to each other.

Radius=?

The magnetic force is given as

F=q V×B

Note that this is a cross product and it is defined as

A×B=|A||B|Sinθ

F=qVB•Sin θ

Since the Velocity has a magnitude of

V=531,000m/s

Also B=21.5×10^-3T

Therefore,

F=qVB•Sin θ

F=1.609×10^-19×531,000×21.5×10^-3Sin90

F=1.84×10^-15N

Then, the Force to keep the body in circular motion is centripetal force

Which is given as

Fc=Mv²/R

Fc=1.67×10^-27×531,000²/R

Fc=4.71×10^-16/R

Here, the magnetic force supplies the centripetal force.

This shows that Fc=F

Fc=F

4.71×10^-16 / R = 1.84×10^-15

Cross multiply

4.71×10^-16= 1.84×10^-15 R

R=4.71^-16/1.84×10^-15

R=0.25597m

R=0.256m

Or

R=255.98mm

The radius of the circular path is approximately 0.256m

answer: cesare beccaria developed the classical school of criminology with from philosopher jeremy bentham

explanation:

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.