(II) A 16-cm-diameter circular loop of wire is placed in a 0.50-T magnetic field. (a) When the p

(II) A 16-cm-diameter circular loop of wire is placed in a...

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the number of magnetic field lines passing through a given area. It is defined as the product of the magnetic field strength, the area the field penetrates, and the cosine of the angle between the magnetic field and the normal to the area. This concept is fundamental in understanding electromagnetic phenomena, including Faraday's law of induction.

Area of a Circular Loop

The area of a circular loop is calculated using the formula A = ?r², where r is the radius of the circle. This calculation is crucial when computing the magnetic flux through a loop, as the area directly influences the total amount of flux intercepted by the loop.

Angle Dependence (Cosine Factor)

The cosine factor in the magnetic flux equation, expressed as cos ?, accounts for the orientation of the loop relative to the magnetic field. When the plane of the loop is rotated, the effective component of the magnetic field perpendicular to the loop's surface changes, thereby altering the flux. This concept highlights the importance of the angle between the field and the normal to the loop in electromagnetic calculations.

Magnetic Field

The magnetic field represents the force field produced by moving electric charges and magnetic materials. It is a vector quantity characterized by both magnitude and direction. In magnetic flux calculations, the strength of the magnetic field is a key parameter, as it determines the density of the magnetic field lines passing through an area.

Transcript

00:01 So in the first part, we are going to use equation 21 .1 to calculate the flux.

00:10 So theta b or this is the flux is equal to b the magnitude of magnetic field times the area of the loop times cosine of theta, where theta is the angle between the field lines, the magnetic field lines and the normal to the plane of the loop.

00:47 So here since the plane of the loop is perpendicular to the field lines, therefore the angle theta, which is the angle between the field lines and the normal to the loop will be equal to 0 degree.

01:03 And hence, cosine of 0 is 1.

01:05 So this equation just becomes b times a.

01:09 Now area is just area of a circle.

01:12 So we put that over the place.

01:16 And now we substitute the value.

01:24 So in the first part, we are going to use equation 21 .1 to calculate the flux.

01:33 So theta b or this is the flux is equal to b the magnitude of magnetic field times the area of the loop times cosine of theta, where theta is the angle between the field lines, the magnetic field lines and the normal to the plane.

01:52 Of the loop.

01:53 So here since the plane of the loop is perpendicular to the field lines, therefore the angle theta, which is the angle between the field lines and the normal to the loop will be for magnetic field and then for the radius of the loop.

02:15 And calculating this we get 1 .005 times 10 to the par minus 2 verb.

02:23 So that's the flux.

02:25 Associated.

02:27 Now in the second part we are said that the plane of the loop is rotated until it makes an angle 42 degree with the field lines.

02:36 So now we have that will to 0 degree and hence cosine of 0 is 1 so this equation just becomes b times a.

02:45 Now area is just area of circles so we put that over the place and now we substitute the values angle between the field lines and the plane of the loop.

02:59 So the angle between the field lines and the normal to the plane of the loop will be 90 degree minus 42 degree.

03:09 So that is equal to 48 degree.

03:13 So that's theta.

03:15 Then again we use the this equation equation 21 .1 to 3 3 .2.

03:27 Calculate the flux for magnetic field and then for the radius of the loop.

03:38 And calculating this, we get 1 .005 times change into the par minus 2 variable.

03:47 So that's the flux associated.

03:50 Now in the second part, we are said that the plane of the loop is rotated until it makes an angle 42 degree with the field lines.

03:59 So now we have the angle between the field lines and the plane of the loop.

04:05 So the angle between the field lines and the normal to the plane of the loop will be 90 degree minus 42 degree.

04:14 So that is equal to 48 degree.

04:18 So that's theta...

Please give Ace some feedback