F = qE + qV × B
where force F, electric field E, velocity V, and magnetic field B are vectors and the × operator is the vector cross product. If the electron remains undeflected, then F = 0 and E = -V × B
which means that |V| = |E| / |B| and the vectors must have the proper geometrical relationship. I therefore get
|V| = 8.8e3 / 3.7e-3
= 2.4e6 m/sec
Acceleration a = V²/r, where r is the radius of curvature.
a = F/m, where m is the mass of an electron,
so qVB/m = V²/r.
Solving for r yields
r = mV/qB
= 9.11e-31 kg * 2.37e6 m/sec / (1.60e-19 coul * 3.7e-3 T)
= 3.65e-3 m
Answer:
The contraction in the rod is 71 mm.
Explanation:
Given that,
original length L'= 2.99 m
Speed 
We need to calculate the length
Using expression for length contraction


Where,

Where, v = speed of observer
c = speed of the light
Put the value into the formula


The expression for the contraction in the rod




Hence, The contraction in the rod is 71 mm.
Answer:
The volume of radius is
× π × radius³ Proved
Explanation:
Given as :
We know that volume of sphere is v =
× π × radius³
Or, v =
× π × r³
Let prove the volume of sphere
So, From the figure of sphere
At the height of z , there is shaded disk with radius x
Let Find the area of triangle with side x , z , r
<u>From Pythagorean theorem</u>
x² + z² = r²
Or, x² = r² - z²
Or, x = 
Now, Area of shaded disk = Area = π × x²
Where x is the radius of disk
Or, Area of shaded disk = π × (
) ²
∴ Area of shaded disk = π × (r² - z²)
Again
<u>If we calculate the area of all horizontal disk, we can get the volume of sphere</u>
So, we simply integrate the area of all disk from - r to + r
i.e volume = 
Or, v =
- 
Or, v = π r² (r + r) - π 
Or, v = π r² (r + r) - π 
Or, v = 2πr³ - π 
Or, v = 2πr³ (
)
Or, v = 2πr³ × 
∴ v =
× π × r³
Hence, The volume of radius is
× π × radius³ Proved . Answer
Answer:
The amount of energy required is 
Explanation:
The energy required to convert the ice to steam is the sum of:
1) Energy required to raise the temperature of the ice from -20 to 0 degree Celsius.
2) Latent heat required to convert the ice into water.
3) Energy required to raise the temperature of water from 0 degrees to 100 degrees
4) Latent heat required to convert the water at 100 degrees to steam.
The amount of energy required in each process is as under
1) 
where
' is specific heat of ice =
2) Amount of heat required in phase 2 equals

3) The amount of heat required to raise the temperature of water from 0 to 100 degrees centigrade equals

where
' is specific heat of water=
4) Amount of heat required in phase 4 equals

Thus the total heat required equals 
At the position of terminal speed the net acceleration of the ball will become zero
As we know that terminal speed will always reach when net force on the ball is zero and its speed will become constant.
So here at this position we can say



now when ball is moving at half of the terminal speed in upward direction then net force on the ball in downwards direction will be


here speed of the ball is half of the terminal speed

then we have


now acceleration will be given as

now we have

downwards