Question

In: Physics

2. Two long coaxial solenoids each carry current I, but in opposite directions, as shown to...

2. Two long coaxial solenoids each carry current I, but in opposite directions, as shown to the right. The solenoids are both

Two long coaxial solenoids each carry current I, but in opposite directions, as shown to the right. The solenoids are both of length L, which can be assumed to be very long, and are centered along the z-axis. The inner solenoid (radius a) has n turns per unit length, and the outer one (radius b) has the same n turns per unit length. 

\(\vec{B}\) inside the inner solenoid, \(=\mathbf{B}_{\text {inner }}=\mu_{0} I\left(n_{1}-n_{2}\right) \mathbf{z} \quad\) And \(\quad \mathbf{B}_{\text {middle }}=-\mu_{0} n_{2} I \hat{z}\)

a) Given

$$ W_{\operatorname{mag}}=\frac{1}{2 \mu_{0}} \int B^{2} d \tau $$

Find the energy stored in this region of space. Why is the answer different from having no inner solenoid?

b). What's the magnetic moment, \(\vec{m}\), of this system?

Solutions

Expert Solution



Related Solutions

Two very long straight wires carry current I in opposite directions as shown below. The distance...
Two very long straight wires carry current I in opposite directions as shown below. The distance from the origin to each of the wires is d. Draw the magnetic field vector on the figure for each of the points listed below. You must indicate both the magnitude and direction of the magnetic field at all points. The origin x=0, y=0 x= 2d, y=0 x= -2d, y=0 x=d, y = -d x= -d, y=d
The two wires carry currents of I = 5.24 A in opposite directions and are separated...
The two wires carry currents of I = 5.24 A in opposite directions and are separated by a distance of d0 = 8.93 cm. Calculate the net magnetic field at a point midway between the wires. Use the direction out of the page as the positive direction and into the page as the negative direction in your answer. Incorrect. Tries 3/20 Previous Tries Calculate the net magnetic field at point P1 - that is 8.62 cm to the right of...
Two solenoids are nested coaxially such that their magnetic fields point in opposite directions. Treat the...
Two solenoids are nested coaxially such that their magnetic fields point in opposite directions. Treat the solenoids as ideal. The outer one has a radius of 20 mm, and the radius of the inner solenoid is 10 mm. The length, number of turns, and current of the outer solenoid are, respectively, 20.3 cm, 553 turns, and 4.17 A. For the inner solenoid the corresponding quantities are 19.3 cm, 383 turns, and 1.35 A. At what speed, v1, should a proton...
Two straight parallel wires carry currents in opposite directions as shown in the figure. One of...
Two straight parallel wires carry currents in opposite directions as shown in the figure. One of the wires carries a current of I2 = 10.2 A. Point A is the midpoint between the wires. The total distance between the wires is d = 12.1 cm. Point C is 5.03 cm to the right of the wire carrying current I2. Current I1 is adjusted so that the magnetic field at C is zero. Calculate the value of the current I1.Calculate the...
1. Two long solenoids are placed in the coaxial position, one inside the other, they have...
1. Two long solenoids are placed in the coaxial position, one inside the other, they have 30 cm and 20 cm diameters, respectively. The outer solenoid is 2 m long with 5000 turns, and carrying a current of 4 A. The inner one is 1 m long with 2000 turns, and carrying a current of 2 A in the opposite sense. Find the magnitude of the magnetic field (in mT) at any point on the solenoid axis inside. A. 10.52...
Two concentric loops of wire are carrying currents in opposite directions as shown in (Figure 2)....
Two concentric loops of wire are carrying currents in opposite directions as shown in (Figure 2). Describe the net force and the torque on either of the current loops. There is a net torque on each loop that causes them to rotate in the same direction. There is a net force on each loop that causes them to repel each other. There is a net torque on each loop that causes them to rotate in opposite directions. There is no net force or torque...
Two very long solenoids have the same number of turns per unit length, and carry the...
Two very long solenoids have the same number of turns per unit length, and carry the same current, but the radius of the cross-section of solenoid #1 is twice that of solenoid #2. How do the magnetic field fluxes through the solenoids compare? Select the best answer. Select the best answer. The flux through solenoid #2 is twice the flux through solenoid #1. They are equal. The flux through solenoid #1 is twice the flux through solenoid #2. The flux...
Two long straight wires separated by 0.10 m carry current in the direction as shown. If...
Two long straight wires separated by 0.10 m carry current in the direction as shown. If I1=12 A and I2= 8 A, find the magnitude and the direction of the net magnetic field a) at point A at a distance of 4 cm from wire 2 in the region between wire 1 and 2 b) at point B at a distance 5 cm left of wire 1.
Two stacked rings have currents in opposite directions as shown. There is a net magnetic force...
Two stacked rings have currents in opposite directions as shown. There is a net magnetic force exerted on the top ring due to the bottom ring. Is which direction is this force? to the right to the left downward upward The net force is zero.
Three long, parallel conductors each carry a current of I = 1.98 A. The figure below...
Three long, parallel conductors each carry a current of I = 1.98 A. The figure below is an end view of the conductors, with each current coming out of the page. Taking a = 1.60 cm, determine the magnitude and direction of the magnetic field at the following points. (a) point A magnitude µT direction ---Select--- to the left to the right toward the top of the page toward the bottom of the page into the page out of the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT