Answer:
Explanation:
a ) No of turns per metre
n = 450 / .35
= 1285.71
Magnetic field inside the solenoid
B = μ₀ n I
Where I is current
B = 4π x 10⁻⁷ x 1285.71 x 1.75
= 28.26 x 10⁻⁴ T
This is the uniform magnetic field inside the solenoid.
b )
Magnetic field around a very long wire at a distance d is given by the expression
B = ( μ₀ /4π ) X 2I / d
= 10⁻⁷ x 2 x ( 1.75 / .01 )
= .35 x 10⁻⁴ T
In the second case magnetic field is much less. It is due to the fact that in the solenoid magnetic field gets multiplied due to increase in the number of turns. In straight coil this does not happen .
Explanation:
It is given that,
Magnetic field, B = 0.5 T
Speed of the proton, v = 60 km/s = 60000 m/s
The helical path followed by the proton shown has a pitch of 5.0 mm, p = 0.005 m
We need to find the angle between the magnetic field and the velocity of the proton. The pitch of the helix is the product of parallel component of velocity and time period. Mathematically, it is given by :





So, the angle between the magnetic field and the velocity of the proton is 50.58 degrees. Hence, this is the required solution.
Effect of temperature.
"If the temperature of the substance is increased then the rate of chemical reaction is also increased because the kinetic energy is greater."
Effect of surface area.
"If the surface area is increased then the rate of reaction is increased because there will be more active sites for the reaction to occur.
Answer:
The answer is "effective stress at point B is 7382 ksi
"
Explanation:
Calculating the value of Compressive Axial Stress:
![\to \sigma y =\frac{F}{A} = \frac{4 F}{( p d ^2 )} = \frac{(4 x ( - 40000 \ lbf))}{[ p \times (1 \ in)^2 ]} = - 50.9 \ ksi \\](https://tex.z-dn.net/?f=%5Cto%20%5Csigma%20y%20%20%3D%5Cfrac%7BF%7D%7BA%7D%20%3D%20%5Cfrac%7B4%20F%7D%7B%28%20p%20d%20%5E2%20%29%7D%20%3D%20%5Cfrac%7B%284%20x%20%28%20-%2040000%20%5C%20lbf%29%29%7D%7B%5B%20p%20%5Ctimes%20%281%20%5C%20in%29%5E2%20%5D%7D%20%3D%20-%2050.9%20%5C%20ksi%20%5C%5C)
Calculating Shear Transverse:



![\to \sigma' =[ s y^2 +3( t \times y^2 + t yz^2 )] \times \frac{1}{2}\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Csigma%27%20%3D%5B%20s%20y%5E2%20%2B3%28%20t%20%5Ctimes%20y%5E2%20%2B%20t%20yz%5E2%20%29%5D%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C)
![= [ (-50.9)^2 +3((63.7)^2 +(0.17)^2 )] \times \frac{1}{2}\\\\=[2590.81+ 3(4057.69)+0.0289]\times \frac{1}{2}\\\\=[2590.81+12,173.07+0.0289] \times \frac{1}{2}\\\\=14763.9089\times \frac{1}{2}\\\\ = 7381.95445 \ ksi\\\\ = 7382 \ ksi](https://tex.z-dn.net/?f=%3D%20%5B%20%28-50.9%29%5E2%20%2B3%28%2863.7%29%5E2%20%2B%280.17%29%5E2%20%29%5D%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D%5B2590.81%2B%203%284057.69%29%2B0.0289%5D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D%5B2590.81%2B12%2C173.07%2B0.0289%5D%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D14763.9089%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%20%3D%207381.95445%20%5C%20ksi%5C%5C%5C%5C%20%3D%207382%20%5C%20ksi)
The heat released by the water when it cools down by a temperature difference

is

where
m=432 g is the mass of the water

is the specific heat capacity of water

is the decrease of temperature of the water
Plugging the numbers into the equation, we find

and this is the amount of heat released by the water.