A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 7.75 cm and inner radius Rb = 3.65 cm. (Figure 1) The central conductor and the conducting tube carry equal currents of I = 3.05 A in opposite directions. The currents are distributed uniformly over the cross-sections of each conductor. What is the value of the magnetic field at a distance r = 5.86 cm from the axis of the conducting tube?
Q1)What is the value of the magnetic field at a distance r = 5.86 cm from the axis of the conducting tube? Recall that μ0=4π×10−7 T⋅m/A.
Solution:
Given that
Solid cylindrical conductor
$$ \begin{array}{l} \mathrm{R}_{\mathrm{a}}=7.75 \mathrm{~cm} \\ \mathrm{R}_{\mathrm{b}}=3.65 \mathrm{~cm} \\ \mathrm{I}=3.05 \mathrm{~A} \\ \mathrm{r}=5.86 \mathrm{~cm} \end{array} $$
Consider the formula for magnetic field is
$$ B=\frac{\mu_{o} I_{e n c}}{2 \pi r} \quad \ldots (1) $$
Consider the formula for area enclosed by the cylinder
$$ A_{c y}=\pi\left(R_{a}^{2}-R_{b}^{2}\right) \ldots (2) $$
Substitute the values in equation (2)
$$ \begin{aligned} A_{c y} &=\pi\left(R_{a}^{2}-R_{b}^{2}\right) \\ &=\pi\left(0.0775^{2}-0.0365^{2}\right) \\ & A_{c y}=0.0146 \mathrm{~m}^{2} \end{aligned} $$
Consider the formula for area enclosed by portion is
$$ A_{p}=\pi\left(r^{2}-R_{b}^{2}\right) \ldots (3) $$
Substitute the values in equation (3)
$$ \begin{aligned} A_{p} &=\pi\left(r^{2}-R_{b}^{2}\right) \\ &=\pi\left(0.0586^{2}-0.0365^{2}\right) \\ & A_{p}=0.0066 \mathrm{~m}^{2} \end{aligned} $$
Consider the formula for current by portion is
$$ I_{p}=I\left(\frac{A_{p}}{A_{c y}}\right) \ldots (4) $$
Substitute the values in equation (4)
$$ \begin{aligned} I_{p} &=3.05\left(\frac{0.0066}{0.0146}\right) \\ &=(3.05 \times 0.4522) \\ & I_{p}=1.379 \mathrm{~A} \end{aligned} $$
Consider the formula for current enclosed by the portion is
$$ I_{e n c}=I-I_{p} \ldots (5) $$
Substitute the values in equation (5)
$$ \begin{aligned} I_{\text {enc }} &=I-I_{p} \\ &=(3.05-1.379) \\ & I_{\text {enc }}=1.67 \mathrm{~A} \end{aligned} $$
Substitute all the values in equation (1)
$$ \begin{aligned} B &=\frac{\mu_{o} I_{\text {erc }}}{2 \pi r} \\ &=\frac{\left(4 \pi \times 10^{-7}\right) 1.67}{2 \pi(0.0586)} \\ &=\frac{\left(2.098 \times 10^{-6}\right)}{0.368} \\ &=\left(5.69 \times 10^{-6}\right) \mathrm{T} \end{aligned} $$
Thus, the magnetic field with distance ris \(\mathrm{B}=5.7 \mu \mathrm{T}\)
A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 5.75 cm and inner radius Rb = 4.95 cm . The central conductor and the conducting tube carry equal currents of I = 3.75 A in opposite directions. The currents are distributed uniformly over the cross-sections of each conductor. What is the value of the magnetic field at a distance r = 5.45 cm from the axis of the...
A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 5.85 cm and inner radius Rb = 4.75 cm . (Figure 1) The central conductor and the conducting tube carry equal currents of I = 1.35 A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance r = 4.99 cm from the...
Learning Goal: To practice Problem-Solving Strategy 28.2 Ampere's Lavw A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra- 6.45 cm and inner radius Rb 5.05 cm (Figure 1) The central conductor and the conducting tube carry equal currents of I 3.05 A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor What is the value of the magnetic field at a distance r...
What will be the integration path used in Ampere's law to calculate the magnetic field B? at a distance r from the axis of the inner cylinder? A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 6.15cm and inner radius Rb = 3.35cm. (Figure 1)The central conductor and the conducting tube carry equal currents of I = 2.85A in opposite directions. The currents are distributed uniformly over the...
A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 7.25cm and inner radius Rb = 4.55cm The central conductor and the conducting tube carry equal currents of I = 1.45A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance r = 5.29cm from the axis of the conducting tube? What is...
Law A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Fe-6.35 cm and inner radius Ri,-4.95 Cm (Figure 1) The central conductor and the conducting tube carry equal currents of I 2.85 A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance 5.93 cm from the axis of the conducting tube? Part C...
please rank largest to smallest for equivalent overlap them PSS 28.2 Ampere's Law 5 of 6 Constar A cyanancas conductor is supported by n aung disks on the axis of a conducting tube with outer radius R = 6.15 cm and inner radius RA335 cm. (Figure 1) The central conductor and the conducting tube carry equal Currents of -3.05 A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of...
"I" in the same direction. oven 1% a. The net magnetic field at a point midway between the two wires. b. The net magnetic field at a point a distance "a" above the upper wire Cl 4. A solid conductor of radius "a" is supported on the axis of a conducting tube with inner radius "b" and outer radius "c". The central conductor and tube carry equal currents "I" in opposite directions. The currents are distributed uniformly over the cross...
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius Rs (called the shield) as shown in Figure 8. The conductors carry equal and opposite currents, I, distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for: (a) r< Ri (b) Ri < R2 Page 2 (c) R2<r<Rs (d) R3 (e) Plot the magnitude...
A coaxial cable is constructed from a central cylindrical conductor of radius rA = 1.40 cm carrying current IA = 7.90 A in the positive x direction and a concentric conducting cylindrical shell with inner radius rB = 14.0 cm and outer radius rC = 15.0 cm with a current of 32.0 A in the negative x direction (see figure below). What are the magnitude and direction of the magnetic field at the following points? = 7.90 A A coaxial...