Answer:
The induced emf is
Explanation:
From the question we are told that
The radius of the circular loop is ![r = 9.50 \ cm = 0.095 \ m](https://tex.z-dn.net/?f=r%20%3D%20%209.50%20%5C%20cm%20%20%3D%20%200.095%20%5C%20m)
The intensity of the wave is ![I = 0.0215 \ W/m^2](https://tex.z-dn.net/?f=I%20%20%3D%20%200.0215%20%5C%20W%2Fm%5E2)
The wavelength is ![\lambda = 6.90\ m](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%206.90%5C%20m)
Generally the intensity is mathematically represented as
![I = \frac{ c * B^2 }{ 2 * \mu_o }](https://tex.z-dn.net/?f=I%20%20%3D%20%20%5Cfrac%7B%20c%20%2A%20%20B%5E2%20%20%7D%7B%202%20%2A%20%5Cmu_o%20%20%7D)
Here
is the permeability of free space with value
![\mu_o = 4 \pi *10^{-7} N/A^2](https://tex.z-dn.net/?f=%5Cmu_o%20%20%3D%20%204%20%5Cpi%20%2A10%5E%7B-7%7D%20N%2FA%5E2)
B is the magnetic field which can be mathematically represented from the equation as
![B = \sqrt{ \frac{ 2 * \mu_o * I }{ c} }](https://tex.z-dn.net/?f=B%20%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B%202%20%2A%20%20%5Cmu_o%20%20%2A%20%20I%20%20%7D%7B%20c%7D%20%7D)
substituting values
![B = \sqrt{ \frac{ 2 * 4\pi *10^{-7} * 0.0215 }{ 3.0*10^{8}} }](https://tex.z-dn.net/?f=B%20%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B%202%20%2A%20%204%5Cpi%20%2A10%5E%7B-7%7D%20%2A%20%20%200.0215%20%20%7D%7B%203.0%2A10%5E%7B8%7D%7D%20%7D)
![B = 1.342 *10^{-8} \ T](https://tex.z-dn.net/?f=B%20%20%3D%20%201.342%20%2A10%5E%7B-8%7D%20%5C%20%20T)
The area is mathematically represented as
![A = \pi r^2](https://tex.z-dn.net/?f=A%20%3D%20%20%5Cpi%20r%5E2)
substituting values
![A = 3.142 * (0.095)^2](https://tex.z-dn.net/?f=A%20%3D%20%203.142%20%2A%20%20%20%280.095%29%5E2)
![A = 0.0284](https://tex.z-dn.net/?f=A%20%3D%200.0284)
The angular velocity is mathematically represented as
![w = 2 * \pi * \frac{c}{\lambda }](https://tex.z-dn.net/?f=w%20%3D%20%202%20%2A%20%20%5Cpi%20%20%2A%20%20%5Cfrac%7Bc%7D%7B%5Clambda%20%7D)
substituting values
Generally the induced emf is mathematically represented as
![\epsilon = N * B * A * w * sin (wt )](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%20%20N%20%2A%20%20B%20%20%2A%20%20A%20%20%2A%20%20w%20%2A%20sin%20%28wt%20%29)
At maximum induced emf ![sin (wt) = 1](https://tex.z-dn.net/?f=sin%20%28wt%29%20%20%3D%20%201)
So
![\epsilon = N * B * A * w](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%20%20N%20%2A%20%20B%20%20%2A%20%20A%20%20%2A%20%20w)
substituting values
Answer:
1) 0.51 seconds.
2) 1.45 m/s.
Explanation:
given, height from which cat falls = 1.3 m
we know that, s = ut +
at².
here if we consider cat moment only in downward direction,
intial velocity of cat in downward direction , u = 0.
so, time, t =
.
⇒ t =
= 0.51 seconds.
t = 0.51 seconds.
now, consider cat moment only in forward direction
s = ut , since acceleration is zero in forward direction
⇒ u =
.
so, u =
= 1.45 m/s .
Answer:
41.4* 10^4 N.m^2/C
Explanation:
given:
E= 4.6 * 10^4 N/C
electric field is 4.6 * 10^4 N/C and square sheet is perpendicular to electric field so, area of vector is parallel to electric field
then electric flux = ∫ E*n dA
= ∫ 4.6 * 10^4 * 3*3
= 41.4* 10^4 N.m^2/C
Let the Blaise runs for time "t" to complete the race
so the total distance he moved is given by
![d_1 = 1* t](https://tex.z-dn.net/?f=d_1%20%3D%201%2A%20t)
Now Issac runs for time t = "t - 2*60"
because it took rest for 2 minutes
![d_2 = 2*(t - 120)](https://tex.z-dn.net/?f=d_2%20%3D%202%2A%28t%20-%20120%29)
now it is given that Blaise wins by 10 m distance
![d_1 - d_2 = 10](https://tex.z-dn.net/?f=d_1%20-%20d_2%20%3D%2010)
![1* t - 2*(t - 120) = 10](https://tex.z-dn.net/?f=1%2A%20t%20-%202%2A%28t%20-%20120%29%20%3D%2010)
![t - 2t + 240 = 10](https://tex.z-dn.net/?f=t%20-%202t%20%2B%20240%20%3D%2010)
![t = 230 s](https://tex.z-dn.net/?f=t%20%3D%20230%20s)
now the distance moved by Blaise is given by
![d_1 = 1*230 = 230 m](https://tex.z-dn.net/?f=d_1%20%3D%201%2A230%20%3D%20230%20m)