Answer:
Part a)

Part B)

Part C)

Explanation:
Part a)
Magnetic field due to a long ideal solenoid is given by

n = number of turns per unit length



now we know that magnetic field due to solenoid is


Now magnetic flux due to this magnetic field is given by




Part B)
Now for mutual inductance we know that




now we have


Part C)
As we know that induced EMF is given as



overuse of a muscle Answer:
Explanation:
Answer:
490N
Explanation:
According Newton's second law!
\sum Force = mass × acceleration
Fm - Ff = ma
Fm is the moving force
Ff s the frictional force = 100N
mass = 65kg
acceleration = 6m/s²
Required
Moving force Fm
Substitute the given force into thr expression and get Fm
Fm -100 = 65(6)
Fm -100 = 390
Fm = 390+100
Fm = 490N
Hence the force that will cause two cart to move is 490N
Answer:
![B_T=2.0*10^-5[-\hat{i}+\hat{j}]T](https://tex.z-dn.net/?f=B_T%3D2.0%2A10%5E-5%5B-%5Chat%7Bi%7D%2B%5Chat%7Bj%7D%5DT)
Explanation:
To find the magnitude of the magnetic field, you use the following formula for the calculation of the magnetic field generated by a current in a wire:

μo: magnetic permeability of vacuum = 4π*10^-7 T/A
I: current = 6.0 A
r: distance to the wire in which magnetic field is measured
In this case, you have four wires at corners of a square of length 9.0cm = 0.09m
You calculate the magnetic field in one corner. Then, you have to sum the contribution of all magnetic field generated by the other three wires, in the other corners. Furthermore, you have to take into account the direction of such magnetic fields. The direction of the magnetic field is given by the right-hand side rule.
If you assume that the magnetic field is measured in the up-right corner of the square, the wire to the left generates a magnetic field (in the corner in which you measure B) with direction upward (+ j), the wire down (down-right) generates a magnetic field with direction to the left (- i) and the third wire generates a magnetic field with a direction that is 45° over the horizontal in the left direction (you can notice that in the image attached below). The total magnetic field will be:
![B_T=B_1+B_2+B_3\\\\B_{T}=\frac{\mu_o I_1}{2\pi r_1}\hat{j}-\frac{\mu_o I_2}{2\pi r_2}\hat{i}+\frac{\mu_o I_3}{2\pi r_3}[-cos45\hat{i}+sin45\hat{j}]](https://tex.z-dn.net/?f=B_T%3DB_1%2BB_2%2BB_3%5C%5C%5C%5CB_%7BT%7D%3D%5Cfrac%7B%5Cmu_o%20I_1%7D%7B2%5Cpi%20r_1%7D%5Chat%7Bj%7D-%5Cfrac%7B%5Cmu_o%20I_2%7D%7B2%5Cpi%20r_2%7D%5Chat%7Bi%7D%2B%5Cfrac%7B%5Cmu_o%20I_3%7D%7B2%5Cpi%20r_3%7D%5B-cos45%5Chat%7Bi%7D%2Bsin45%5Chat%7Bj%7D%5D)
I1 = I2 = I3 = 6.0A
r1 = 0.09m
r2 = 0.09m

Then you have:
![B_T=\frac{\mu_o I}{2\pi}[(-\frac{1}{r_2}-\frac{cos45}{r_3})\hat{i}+(\frac{1}{r_1}+\frac{sin45}{r_3})\hat{j}}]\\\\B_T=\frac{(4\pi*10^{-7}T/A)(6.0A)}{2\pi}[(-\frac{1}{0.09m}-\frac{cos45}{0.127m})\hat{i}+(\frac{1}{0.09m}+\frac{sin45}{0.127m})]\\\\B_T=\frac{(4\pi*10^{-7}T/A)(6.0A)}{2\pi}[-16.67\hat{i}+16.67\hat{j}]\\\\B_T=2.0*10^-5[-\hat{i}+\hat{j}]T](https://tex.z-dn.net/?f=B_T%3D%5Cfrac%7B%5Cmu_o%20I%7D%7B2%5Cpi%7D%5B%28-%5Cfrac%7B1%7D%7Br_2%7D-%5Cfrac%7Bcos45%7D%7Br_3%7D%29%5Chat%7Bi%7D%2B%28%5Cfrac%7B1%7D%7Br_1%7D%2B%5Cfrac%7Bsin45%7D%7Br_3%7D%29%5Chat%7Bj%7D%7D%5D%5C%5C%5C%5CB_T%3D%5Cfrac%7B%284%5Cpi%2A10%5E%7B-7%7DT%2FA%29%286.0A%29%7D%7B2%5Cpi%7D%5B%28-%5Cfrac%7B1%7D%7B0.09m%7D-%5Cfrac%7Bcos45%7D%7B0.127m%7D%29%5Chat%7Bi%7D%2B%28%5Cfrac%7B1%7D%7B0.09m%7D%2B%5Cfrac%7Bsin45%7D%7B0.127m%7D%29%5D%5C%5C%5C%5CB_T%3D%5Cfrac%7B%284%5Cpi%2A10%5E%7B-7%7DT%2FA%29%286.0A%29%7D%7B2%5Cpi%7D%5B-16.67%5Chat%7Bi%7D%2B16.67%5Chat%7Bj%7D%5D%5C%5C%5C%5CB_T%3D2.0%2A10%5E-5%5B-%5Chat%7Bi%7D%2B%5Chat%7Bj%7D%5DT)