In Fig. 29-39, two circular arcs have radii a=13.5 cm and b= 10.7 cm, subtend angle θ=74.0^∘, ca

step 1 a given problem there are two circular arc which are connected to each other like this both are

In Fig. 29-39, two circular arcs have radii a=13.5 cm and b=...

Key Concepts

Right-Hand Rule

The right-hand rule is used to determine the direction of the magnetic field generated by a current. By positioning the thumb in the direction of the current and curling the fingers, one can deduce the orientation of the resulting magnetic field. This concept is crucial for understanding not only the magnitude but also the directional properties of the magnetic field in problems involving current-carrying conductors.

Biot-Savart Law

This law describes how a current element produces a magnetic field in space. It forms the basis for calculating the magnetic field generated by a current-carrying conductor by integrating the contributions from each element of the current. In problems involving curved conductors, the Biot-Savart law is essential for setting up the integration and understanding how the geometry influences the magnetic field.

Magnetic Field from a Circular Arc

When a current flows along a circular arc, the magnetic field at the center of curvature can be calculated using a simplified form of the Biot-Savart law, resulting in a formula that involves the magnitude of the current, the subtended angle (in radians), the radius of the arc, and the permeability of free space. This concept is crucial as it shows how partial loops contribute to the field, a common element in many electromagnetic applications.

Superposition Principle in Electromagnetism

This principle states that the net magnetic field created by multiple current segments is the vector sum of the individual magnetic fields produced by each segment. It is a fundamental concept in solving complex current distributions, as it allows for the independent calculation of fields from different sources before combining them to find the overall field.

Transcript

00:01 Hi given problem there are two circular art which are connected each other like this, both or having a common center.

00:21 Mm and but i fasting too.

00:31 These two circular are in a blog wise direct and videos of the outer circular arc is even as a whose value is is equal 13.5 centimetre or this is 13.5 10 for -2 m radius of the inner are smaller art that is b whose values given us then 0.7 centimetre.

01:15 Or and they went into and this par -2 m.

01:22 The value of current passing through this loop is 0.411 here.

01:30 And this sector angle the doctor is 74°. so we have to find net magnetic field this form in st pete.

01:41 So it should be clear that there will be zero magnetic field because of these radial waves that man magnetic.

01:49 We will be only because of are mhm course.

01:54 And to find this magnetically we use expression for the magnetic will do to anarcho cetera angle is that has given us data by 3° little mu not by by two times of the radio.

02:14 Yeah the two magnetic fields here.

02:16 First you to the r.

02:18 Who's really as you say e.

02:20 A.

02:20 That will be given as peter by 3 60°. but um you not i by two times of its serious.

02:30 Which is a.

02:31 And that will do you do are having a radius b will be given as b.

02:37 B.

02:38 It'll be peter by 3 60°. who knew not i by two times of experience which is b.

02:47 As this magnet will defend universally on the radio.

02:54 The magnetic group due to the smaller are maybe more and that bigger are the net magnetic field will be given by mhm b minus mm is this is pita by 360° and mu not and i.

03:14 And by two peace.

03:16 The things these few things can be taken as a comin out leaving behind one by the -1 x eight.

03:25 But before finding the net value of this magnetic where we could find the directions of these magnetic fields...

Please give Ace some feedback