<span>Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.</span>
Answer:
If I double the current in the inductor, the new total energy will become 4E (option f).
Explanation:
The coil or inductor is a passive component made of an insulated wire that stores energy in the form of a magnetic field due to its form of coiled turns of wire, through a phenomenon called self-induction. In other words, inductors store energy in the form of a magnetic field. The energy stored in the space where there is a magnetic field in the inductor is:
![E=\frac{1}{2} *L*I^{2}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1%7D%7B2%7D%20%2AL%2AI%5E%7B2%7D)
where E is Energy [J], L is Inductance [H] and I is Current [A].
If you double the current in the inductor, then the new value of the current is I'= 2*I. So replacing the new total energy is:
![E'=\frac{1}{2} *L*I'^{2}=\frac{1}{2} *L*(2*I)^{2}=\frac{1}{2} *L*4*I^{2}=4*\frac{1}{2} *L*I^{2}](https://tex.z-dn.net/?f=E%27%3D%5Cfrac%7B1%7D%7B2%7D%20%2AL%2AI%27%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2AL%2A%282%2AI%29%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2AL%2A4%2AI%5E%7B2%7D%3D4%2A%5Cfrac%7B1%7D%7B2%7D%20%2AL%2AI%5E%7B2%7D)
Then:
![E'=4*E](https://tex.z-dn.net/?f=E%27%3D4%2AE)
<em><u>If I double the current in the inductor, the new total energy will become 4E (option f).</u></em>
Answer:
84.82N/C.
Explanation:
The x-components of the electric field cancel; therefore, we only care about the y-components.
The y-component of the differential electric field at the center is
.
Now, let us call
the charge per unit length, then we know that
;
therefore,
![$dE = \frac{k \lambda R d\theta }{R^2} sin(\theta )$](https://tex.z-dn.net/?f=%24dE%20%3D%20%5Cfrac%7Bk%20%5Clambda%20R%20d%5Ctheta%20%7D%7BR%5E2%7D%20sin%28%5Ctheta%20%29%24)
![$dE = \frac{k \lambda d\theta }{R} sin(\theta )$](https://tex.z-dn.net/?f=%24dE%20%3D%20%5Cfrac%7Bk%20%5Clambda%20%20d%5Ctheta%20%7D%7BR%7D%20sin%28%5Ctheta%20%29%24)
Integrating
![$E = \frac{k \lambda }{R}\int_0^\pi sin(\theta )d\theta$](https://tex.z-dn.net/?f=%24E%20%3D%20%5Cfrac%7Bk%20%5Clambda%20%20%20%7D%7BR%7D%5Cint_0%5E%5Cpi%20sin%28%5Ctheta%20%29d%5Ctheta%24)
![$E = \frac{k \lambda }{R}*[-cos(\pi )+cos(0) ]$](https://tex.z-dn.net/?f=%24E%20%3D%20%5Cfrac%7Bk%20%5Clambda%20%20%20%7D%7BR%7D%2A%5B-cos%28%5Cpi%20%29%2Bcos%280%29%20%5D%24)
![$E = \frac{2k \lambda }{R}.$](https://tex.z-dn.net/?f=%24E%20%3D%20%5Cfrac%7B2k%20%5Clambda%20%20%20%7D%7BR%7D.%24)
Now, we know that
![\lambda = 3.0*10^{-9}C/m,](https://tex.z-dn.net/?f=%5Clambda%20%3D%203.0%2A10%5E%7B-9%7DC%2Fm%2C)
![k = 9*10^9kg\cdot m^3\cdot s^{-4}\cdot A^{-2},](https://tex.z-dn.net/?f=k%20%3D%209%2A10%5E9kg%5Ccdot%20m%5E3%5Ccdot%20s%5E%7B-4%7D%5Ccdot%20A%5E%7B-2%7D%2C)
and the radius of the semicircle is
![\pi R = 2.0m,\\\\R = \dfrac{2.0m}{\pi };](https://tex.z-dn.net/?f=%5Cpi%20R%20%3D%202.0m%2C%5C%5C%5C%5CR%20%3D%20%5Cdfrac%7B2.0m%7D%7B%5Cpi%20%7D%3B)
therefore,
![$E = \frac{2(9*10^9) (3.0*10^{-9}) }{\dfrac{2.0}{\pi } }.$](https://tex.z-dn.net/?f=%24E%20%3D%20%5Cfrac%7B2%289%2A10%5E9%29%20%283.0%2A10%5E%7B-9%7D%29%20%20%20%7D%7B%5Cdfrac%7B2.0%7D%7B%5Cpi%20%7D%20%7D.%24)
![$\boxed{E = 84.82N/C.}$](https://tex.z-dn.net/?f=%24%5Cboxed%7BE%20%3D%2084.82N%2FC.%7D%24)
Answer:
the similarity is that hands are applied and force