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Chapter 29: Q50P (page 861)

A solenoid that is 95.0cmlong has a radius of2.00cmand a winding ofrole="math" localid="1663136568607" 1200turns; it carries a current of3.60A. Calculate the magnitude of the magnetic field inside the solenoid.

Short Answer

Expert verified

The magnitude of the magnetic field inside the solenoid is 0.00571T.

Step by step solution

01

Listing the given quantities

l=95cm=0.95m

N=1200

i=3.60A

02

Understanding the concept of magnetic field and toroid 

The magnetic field produced by the solenoid is given as,

B=μ0in=μ0i(Nl)

Here, B is the magnetic field, i is current, n is the number of turns per unit length, N is the total number of turns and l is the length of the solenoid.

We can calculate the magnetic field due to an ideal solenoid. In our case, the solenoid is having a definite length, so we use this equation to calculate the magnetic field inside the solenoid.

03

Calculating the magnetic field inside the solenoid.

By using the equation,we can calculate the magnetic field.

B=μ0in=μ0iNl=1.26×10−6×3.60×12000.95=0.00571T

Therefore, the magnitude of the magnetic field inside the solenoid is 0.00571T.

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Most popular questions from this chapter

A long vertical wire carries an unknown current. Coaxial with the wire is a long, thin, cylindrical conducting surface that carries a current of30 mAupward. The cylindrical surface has a radius of3.0 mm. If the magnitude of the magnetic field at a point5.0 mmfrom the wire is1.0μT, (a) What are the size and(b) What is the direction of the current in the wire?

Question: In Figure, current I=56.2mAis set up in a loop having two radial lengths and two semicircles of radiia=5.72cm andb=9.36cm with a common centerP(a) What are the magnitude and (b) What are the direction (into or out of the page) of the magnetic field at P and the (c) What is the magnitude of the loop’s magnetic dipole moment? and (d) What is the direction of the loop’s magnetic dipole moment?

Figure 29-73a shows a length of wire carrying a currentiand bent into a circular coil of one turn. In Fig. 29-73b the same length of wire has been bent to give a coil of two turns, each of half the original radius. (a) IfBaare Bbthe magnitudes of the magnetic fields at the centers of the two coils, what is the ratio BbBa? (b) What is the ratioμbμaof the dipole moment magnitudes of the coils?

Two long straight wires are parallel and 8.0cmapart .They are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 300μT. (a) Should the currents be in the same or opposite directions? (b) How much current is needed?

In Fig. 29-54a, wire 1 consists of a circular arc and two radial lengths; it carries currenti1=0.50Ain the direction indicated. Wire 2, shown in cross section, is long, straight, and Perpendicular to the plane of the figure. Its distance from the center of the arc is equal to the radius Rof the arc, and it carries a current i2 that can be varied. The two currents set up a net magnetic fieldB⇀at the center of the arc. Figure bgives the square of the field’s magnitude B2 plotted versus the square ofthe currenti22. The vertical scale is set byBs2=10.0×10-10T2what angle is subtended by the arc?
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