Answer:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Explanation:
In order to use the rule of thumb to find the speed of sound in meters per second, we need to use some conversion ratios. We know there is 1 mile per every 5 seconds after the lightning is seen. We also know that there are 5280ft in 1 mile and we also know that there are 0.3048m in 1ft. This is enough information to solve this problem. We set our conversion ratios like this:
notice how the ratios were written in such a way that the units got cancelled when calculating them. Notice that in one ratio the miles were on the numerator of the fraction while on the other they were on the denominator, which allows us to cancel them. The same happened with the feet.
The problem asks us to express the answer to one significant figure so the speed of sound rounds to 300m/s.
For the second part of the problem we need to use conversions again. This time we will write our ratios backwards and take into account that there are 1000m to 1 km, so we get:
This means that for every 3.11s there will be a distance of 1km from the place where the lightning stroke. Since this is a rule of thumb, we round to the nearest integer for the calculations to be made easily, so the rule goes like this:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Answer:
the maximum intensity of an electromagnetic wave at the given frequency is 45 kW/m²
Explanation:
Given the data in the question;
To determine the maximum intensity of an electromagnetic wave, we use the formula;
= 
ε₀cE
²
where ε₀ is permittivity of free space ( 8.85 × 10⁻¹² C²/N.m² )
c is the speed of light ( 3 × 10⁸ m/s )
E is the maximum magnitude of the electric field
first we calculate the maximum magnitude of the electric field ( E )
E = 350/f kV/m
given that frequency of 60 Hz, we substitute
E = 350/60 kV/m
E = 5.83333 kV/m
E = 5.83333 kV/m × ( 
)
E = 5833.33 N/C
so we substitute all our values into the formula for intensity of an electromagnetic wave;
= ε₀cE²
= × ( 8.85 × 10⁻¹² C²/N.m² ) × ( 3 × 10⁸ m/s ) × ( 5833.33 N/C )²
= 45 × 10³ W/m²
= 45 × 10³ W/m² × ( 
)
= 45 kW/m²
Therefore, the maximum intensity of an electromagnetic wave at the given frequency is 45 kW/m²
Answer:
Part a)
Part b)
Explanation:
Part a)
As we know that electric field intensity due to some given charge distribution is given as
now electric flux through a spherical surface of radius r is given as
now by Guass law we know that
now volume charge density is given as
Part b)
Total charge inside the radius R is given as
Answer:
The electric potential at the center of the meter stick is 54 KV.
Explanation:
Electric potential (V) is given as:
i.e V = 
Where: k is the Coulomb constant, q is the charge and r is the distance.
Given: q = 3.0 μC = 3.0 x 
C, r = 0.5 m
So that,
V = 
= 
V = 54000
= 54 000 volts
The electric potential at the center of the meter stick is 54 KV.
Answer:
Explanation:
Generally, length of vector means the magnitude of the vector.
So, given a vector
R = a•i + b•j + c•k
Then, it magnitude can be caused using
|R|= √(a²+b²+c²)
So, applying this to each of the vector given.
(a) 2i + 4j + 3k
The length is
L = √(2²+4²+3²)
L = √(4+16+9)
L = √29
L = 5.385 unit
(b) 5i − 2j + k
Note that k means 1k
The length is
L = √(5²+(-2)²+1²)
Note that, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
Note that, since there is no component j implies that j component is 0
L = 2i + 0j - 1k
The length is
L = √(2²+0²+(-1)²)
L = √(4+0+1)
L = √5
L = 2.236 unit
(d) 5i
Same as above no is j-component and k-component
L = 5i + 0j + 0k
The length is
L = √(5²+0²+0²)
L = √(25+0+0)
L = √25
L = 5 unit
(e) 3i − 2j − k
The length is
L = √(3²+(-2)²+(-1)²)
L = √(9+4+1)
L = √14
L = 3.742 unit
(f) i + j + k
The length is
L = √(1²+1²+1²)
L = √(1+1+1)
L = √3
L = 1.7321 unit
