Answer:
The electric field at origin is 3600 N/C
Solution:
As per the question:
Charge density of rod 1, ![\lambda = 1\ nC = 1\times 10^{- 9}\ C](https://tex.z-dn.net/?f=%5Clambda%20%3D%201%5C%20nC%20%3D%201%5Ctimes%2010%5E%7B-%209%7D%5C%20C)
Charge density of rod 2, ![\lambda = - 1\ nC = - 1\times 10^{- 9}\ C](https://tex.z-dn.net/?f=%5Clambda%20%3D%20-%201%5C%20nC%20%3D%20-%201%5Ctimes%2010%5E%7B-%209%7D%5C%20C)
Now,
To calculate the electric field at origin:
We know that the electric field due to a long rod is given by:
![\vec{E} = \frac{\lambda }{2\pi \epsilon_{o}{R}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20%5Cfrac%7B%5Clambda%20%7D%7B2%5Cpi%20%5Cepsilon_%7Bo%7D%7BR%7D)
Also,
(1)
where
K = electrostatic constant = ![\frac{1}{4\pi \epsilon_{o} R}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon_%7Bo%7D%20R%7D)
R = Distance
= linear charge density
Now,
In case, the charge is positive, the electric field is away from the rod and towards it if the charge is negative.
At x = - 1 cm = - 0.01 m:
Using eqn (1):
![\vec{E} = \frac{2\times 9\times 10^{9}\times 1\times 10^{- 9}}{0.01} = 1800\ N/C](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20%5Cfrac%7B2%5Ctimes%209%5Ctimes%2010%5E%7B9%7D%5Ctimes%201%5Ctimes%2010%5E%7B-%209%7D%7D%7B0.01%7D%20%3D%201800%5C%20N%2FC)
(towards)
Now, at x = 1 cm = 0.01 m :
Using eqn (1):
![\vec{E'} = \frac{2\times 9\times 10^{9}\times - 1\times 10^{- 9}}{0.01} = - 1800\ N/C](https://tex.z-dn.net/?f=%5Cvec%7BE%27%7D%20%3D%20%5Cfrac%7B2%5Ctimes%209%5Ctimes%2010%5E%7B9%7D%5Ctimes%20-%201%5Ctimes%2010%5E%7B-%209%7D%7D%7B0.01%7D%20%3D%20-%201800%5C%20N%2FC)
(towards)
Now, the total field at the origin is the sum of both the fields:
![\vec{E_{net}} = 1800 + 1800 = 3600\ N/C](https://tex.z-dn.net/?f=%5Cvec%7BE_%7Bnet%7D%7D%20%3D%201800%20%2B%201800%20%3D%203600%5C%20N%2FC)
I believe the correct answer among the choices listed is option C. The four components of a controlled experiment are the independent variable, dependent variable, control, constant. A controlled experiment is a test where a researcher vary one variable at a time.<span>
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Answer:
The orbital speed is approximately 17,325.57 m/s
The number of Earth days it would take lo to complete its orbit is approximately 1.77 days
Explanation:
The given parameters are;
The mass of lo, m ≈ 7.22 × 10²² kg
The radius of lo, R ≈ 1.82 × 10⁶ m
The mean distance between Jupiter and lo = 4.22 × 10⁸ m
The orbital equation is given as follows;
![\dfrac{m \cdot v^2}{R} = \dfrac{G \times M \times m}{R^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm%20%5Ccdot%20v%5E2%7D%7BR%7D%20%3D%20%5Cdfrac%7BG%20%5Ctimes%20M%20%5Ctimes%20m%7D%7BR%5E2%7D)
![\therefore v = \sqrt{\dfrac{G \cdot M}{R} } = \sqrt{\dfrac{ 6.67408 \times 10^{-11} \times 1.898 \times 10^{27}}{4.22 \times 10^8} } = 17,325.57 \ m/s](https://tex.z-dn.net/?f=%5Ctherefore%20v%20%3D%20%5Csqrt%7B%5Cdfrac%7BG%20%5Ccdot%20M%7D%7BR%7D%20%7D%20%3D%20%5Csqrt%7B%5Cdfrac%7B%206.67408%20%5Ctimes%2010%5E%7B-11%7D%20%20%5Ctimes%201.898%20%5Ctimes%2010%5E%7B27%7D%7D%7B4.22%20%5Ctimes%2010%5E8%7D%20%7D%20%20%3D%2017%2C325.57%20%5C%20m%2Fs)
The orbital speed ≈ 17,325.57 m/s
The time to complete one orbit = (2 × π × 4.22 × 10⁸)/(17325.57) ≈ 153039.94 s
The time to complete one orbit ≈ 153039.94 s ≈ 1.77 days
The number of Earth days it would take lo to complete its orbit ≈ 1.77 days.