Answer:
The magnitude of electron acceleration is
![\frac{m}{s^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D)
Explanation:
Given:
Distance from the wire to the field point
m
Speed of electron ![v = 35.5 \%c](https://tex.z-dn.net/?f=v%20%3D%2035.5%20%5C%25c)
Current
A
For finding the acceleration,
First find the magnetic field due to wire,
![B = \frac{\mu _{o}I }{2\pi r }](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%5Cmu%20_%7Bo%7DI%20%7D%7B2%5Cpi%20r%20%7D)
Where ![\mu_{o} = 4\pi \times 10^{-7}](https://tex.z-dn.net/?f=%5Cmu_%7Bo%7D%20%3D%204%5Cpi%20%20%20%5Ctimes%2010%5E%7B-7%7D)
![B = \frac{4\pi \times 10^{-7} \times 17.7 }{2\pi (2.83 \times 10^{-2} ) }](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%20%20%5Ctimes%2017.7%20%7D%7B2%5Cpi%20%282.83%20%5Ctimes%2010%5E%7B-2%7D%20%29%20%7D)
T
The magnetic force exerted on the electron passing through straight wire,
![F = 1.6 \times 10^{-19} \times 0.355 \times 3 \times 10^{8} \times 12.50 \times 10^{-5}](https://tex.z-dn.net/?f=F%20%3D%201.6%20%5Ctimes%2010%5E%7B-19%7D%20%5Ctimes%200.355%20%5Ctimes%203%20%5Ctimes%2010%5E%7B8%7D%20%5Ctimes%2012.50%20%5Ctimes%2010%5E%7B-5%7D)
N
From the newton's second law
![F = ma](https://tex.z-dn.net/?f=F%20%3D%20ma)
Where
mass of electron
kg
So acceleration is given by,
![a = \frac{F}{m}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7BF%7D%7Bm%7D)
![a = \frac{21.3 \times 10^{-16} }{9.1 \times 10^{-31} }](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B21.3%20%5Ctimes%2010%5E%7B-16%7D%20%7D%7B9.1%20%5Ctimes%2010%5E%7B-31%7D%20%7D)
![\frac{m}{s^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D)
Therefore, the magnitude of electron acceleration is
![\frac{m}{s^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%20%7D)
Explanation:
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
Formula
Newton's Second Law
F = m * a
F = force
m = mass of an object
a = acceleration
I think it is option (C).
If the answer is helpful then mark me as brainly.
Answer:
B = 0.8 T
Explanation:
It is given that,
Radius of circular loop, r = 0.75 m
Current in the loop, I = 3 A
The loop may be rotated about an axis that passes through the center and lies in the plane of the loop.
When the orientation of the normal to the loop with respect to the direction of the magnetic field is 25°, the torque on the coil is 1.8 Nm.
We need to find the magnitude of the uniform magnetic field exerting this torque on the loop. Torque acting on the loop is given by :
![\tau=NIAB\sin\theta](https://tex.z-dn.net/?f=%5Ctau%3DNIAB%5Csin%5Ctheta)
B is magnetic field
![B=\dfrac{\tau}{NIA\sin\theta}\\\\B=\dfrac{1.8}{1\times \pi \times (0.75)^2\times 3\times \sin(25)}\\\\B=0.8\ T](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Ctau%7D%7BNIA%5Csin%5Ctheta%7D%5C%5C%5C%5CB%3D%5Cdfrac%7B1.8%7D%7B1%5Ctimes%20%5Cpi%20%5Ctimes%20%280.75%29%5E2%5Ctimes%203%5Ctimes%20%5Csin%2825%29%7D%5C%5C%5C%5CB%3D0.8%5C%20T)
So, the magnitude of the uniform magnetic field exerting this torque on the loop is 0.8 T.
Answer:
The minimum inductance needed is 2.78 H
Explanation:
Given;
frequency of the AC, f = 26.5 Hz
the root mean square voltage in the circuit,
= 41.2 V
the maximum current in the circuit, I₀ = 126 mA
The root mean square current is given by;
![I_{rms} = \frac{I_o}{\sqrt{2} } \\\\I_{rms} = \frac{126*10^{-3}}{\sqrt{2} }\\\\I_{rms} =0.0891 \ A](https://tex.z-dn.net/?f=I_%7Brms%7D%20%3D%20%5Cfrac%7BI_o%7D%7B%5Csqrt%7B2%7D%20%7D%20%5C%5C%5C%5CI_%7Brms%7D%20%20%3D%20%5Cfrac%7B126%2A10%5E%7B-3%7D%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C%5C%5CI_%7Brms%7D%20%20%3D0.0891%20%5C%20A)
The inductive reactance is given by;
![X_l = \frac{V_{rms}}{I_{rms}} \\\\X_l= \frac{41.2}{0.0891}\\\\X_l = 462.4 \ ohms](https://tex.z-dn.net/?f=X_l%20%3D%20%5Cfrac%7BV_%7Brms%7D%7D%7BI_%7Brms%7D%7D%20%5C%5C%5C%5CX_l%3D%20%5Cfrac%7B41.2%7D%7B0.0891%7D%5C%5C%5C%5CX_l%20%3D%20462.4%20%5C%20ohms)
The minimum inductance needed is given by;
![X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2\pi f}\\\\L = \frac{462.4}{2\pi *26.5}\\\\L = 2.78 \ H](https://tex.z-dn.net/?f=X_l%20%3D%20%5Comega%20L%5C%5C%5C%5CX_l%20%3D%202%5Cpi%20%20fL%5C%5C%5C%5CL%20%3D%20%5Cfrac%7BX_l%7D%7B2%5Cpi%20f%7D%5C%5C%5C%5CL%20%3D%20%5Cfrac%7B462.4%7D%7B2%5Cpi%20%2A26.5%7D%5C%5C%5C%5CL%20%3D%202.78%20%5C%20H)
Therefore, the minimum inductance needed is 2.78 H