Doc: Toroid Class 12 Notes | EduRev

Physics Class 12

Created by: Infinity Academy

Class 12 : Doc: Toroid Class 12 Notes | EduRev

The document Doc: Toroid Class 12 Notes | EduRev is a part of the Class 12 Course Physics Class 12.
All you need of Class 12 at this link: Class 12

9. Toroid : It is on hollow circular tube have windings of conducting wire closely attached to each other circularly on it (as shown below)

Doc: Toroid Class 12 Notes | EduRev

for ideal Toroid d << R

Magnetic field in Toroid

Let N = Total No. of turns

Now from Ampere's circuital law

Doc: Toroid Class 12 Notes | EduRev   

B.2πR = μ0 iin = μ0 Ni       

⇒ B = Doc: Toroid Class 12 Notes | EduRev     

Doc: Toroid Class 12 Notes | EduRev

n = Doc: Toroid Class 12 Notes | EduRev = No of turns per unit length

so B = μ0 n i

10. Infinite Current Carrying sheet

Now from Ampere's loop

Doc: Toroid Class 12 Notes | EduRev

Doc: Toroid Class 12 Notes | EduRev

Doc: Toroid Class 12 Notes | EduRev 

Bl + 0 + Bl + 0 = μ l  
Doc: Toroid Class 12 Notes | EduRev

B = Doc: Toroid Class 12 Notes | EduRev

Ex.14 Three identical long solenoids P, Q and R are connected to each other as shown in figure. if the magnetic field at the center of P is 2.0 T, what would be the field at the centre of Q? Assume that the field due to any solenoid is confined within the volume of that solenoid only.

Sol. Doc: Toroid Class 12 Notes | EduRev

As the solenoids are identical, the currents in Q and R will be the same and will be half the current in P. The magnetic field within a solenoid is given by B = μ0 ni. Hence the field in Q will be equal to the field in R and will be half the field in P i.e., will be 1.0 T

11. Magnetic force on moving charge

When a charge q moves with velocity Doc: Toroid Class 12 Notes | EduRev, in a magnetic field Doc: Toroid Class 12 Notes | EduRev, then the magnetic force experienced by moving charge is given by following formula :

Doc: Toroid Class 12 Notes | EduRev Put q with sign. ...(9)

Doc: Toroid Class 12 Notes | EduRev : Instantaneous velocity

Doc: Toroid Class 12 Notes | EduRev : Magnetic field at that point.

11.1 DIFFERENCE BETWEEN MAGNETIC FORCE AND ELECTRIC FORCE

(1) Magentic force is always perpendicular to the field while electric force is collinear with the field.

(2) Magnetic force is velocity dependent, i.e., acts only when the charged particle is in motion while electric force (qE) is independent of the state of rest or motion of the charged particle.

(3) Magentic force does no work when the charged particle is displaced while the electric force does work in displacing the charged particle.

Note :

Doc: Toroid Class 12 Notes | EduRev

Therefore, Doc: Toroid Class 12 Notes | EduRev Therefore, power due to magnetic force on a charged particle is zero. (use the formula of power P = Doc: Toroid Class 12 Notes | EduRevfor its proof)

Since the Doc: Toroid Class 12 Notes | EduRev so work done by magnetic force is zero in every part of the motion. The magnetic force cannot increase or decrease the speed (or kinetic energy) of a charged particle. Its can only change the direction of velocity.

On a stationary charged particle, magnetic force is zero.

If Doc: Toroid Class 12 Notes | EduRev, then also magnetic force on charged particle is zero. It moves along a straight line if only magnetic field is acting.

Ex.15 A Charged particle of mass 5 mg and charge q = +2μC has velocity Doc: Toroid Class 12 Notes | EduRev. Find out the magnetic force on the charged particle and its acceleration at this instant due to magnetic field Doc: Toroid Class 12 Notes | EduRevDoc: Toroid Class 12 Notes | EduRev and Doc: Toroid Class 12 Notes | EduRev are in m/s and Wb/m2 respectively.

Sol. Doc: Toroid Class 12 Notes | EduRev = 2 × 10-6 Doc: Toroid Class 12 Notes | EduRev

By Newton's Law Doc: Toroid Class 12 Notes | EduRev

=Doc: Toroid Class 12 Notes | EduRev

Ex.16 A charged particle has acceleration Doc: Toroid Class 12 Notes | EduRev in a magnetic field Doc: Toroid Class 12 Notes | EduRev. Find the value of x.

Sol. Doc: Toroid Class 12 Notes | EduRev Doc: Toroid Class 12 Notes | EduRev

Therefore, Doc: Toroid Class 12 Notes | EduRev

Therefore, Doc: Toroid Class 12 Notes | EduRev

Therefore, Doc: Toroid Class 12 Notes | EduRev = 0

⇒ - 6 + 2x = 0 ⇒ x = 3.

12. MOTION OF A CHARGED PARTICLE IN A UNIFORM MAGNETIC FIELD.

12.1 WHEN THE CHARGED PARTICLE IS GIVEN VELOCITY PERPENDICULAR TO THE FIELD

Let a particle of charged q and mass m is moving with a velocity v and enters at right angles to a uniform magnetic field Doc: Toroid Class 12 Notes | EduRev as shown in figure.

The force on the particle is qvB and this force will always act in a direction perpendicular to v. Hence, the particle will move on a circular path. If the radius of the path is r then

Doc: Toroid Class 12 Notes | EduRev

Doc: Toroid Class 12 Notes | EduRev or, r = Doc: Toroid Class 12 Notes | EduRev ...(10)

Thus, radius of the path is proportional to the momentum mv of the particle and inversely proportional to the magnitude of magnetic field.

Time period : The time period is the time taken by the charged particle to complete one rotation of the circular path which is given by,

T = Doc: Toroid Class 12 Notes | EduRev = Doc: Toroid Class 12 Notes | EduRev ...(11)

The time period is independent of the speed v.

Frequency : The frequency is number of revolution of charged particle in one second, which is given by,

Doc: Toroid Class 12 Notes | EduRev..(12)

and angular frequency = Doc: Toroid Class 12 Notes | EduRev

Ex 17. A proton (p), a - particle and deuteron (D) are moving in circular paths with same kinetic energies in the same magnetic field. Find the ratio of their radii and time periods. (Neglect interaction between particles).

Sol. R = Doc: Toroid Class 12 Notes | EduRev

Therefore, Rp : Ra : RD =Doc: Toroid Class 12 Notes | EduRev

= 1 : 1 : Doc: Toroid Class 12 Notes | EduRev

T = 2πm/qB

Therefore, Tp : Ta : TDoc: Toroid Class 12 Notes | EduRev : Doc: Toroid Class 12 Notes | EduRev : Doc: Toroid Class 12 Notes | EduRev

= 1 : 2 : 2 Ans.

Ex.18 A positive charge particle of charge q, mass m enters into a uniform magnetic field with velocity v as shown in the figure. There is no magnetic field to the left of PQ. Find

 Doc: Toroid Class 12 Notes | EduRev

(i) time spent,

(ii) distance travelled in the magnetic field

(iii) impulse of magnetic force.

Sol. The particle will move in the field as shown. Angle subtended by the arc at the centre = 2q

(i) Time spent by the charge in magnetic field

wt = q ⇒ Doc: Toroid Class 12 Notes | EduRev ⇒ t = Doc: Toroid Class 12 Notes | EduRev

(ii) Distance travelled by the charge in magnetic field : 

= r (2θ) = Doc: Toroid Class 12 Notes | EduRev 
Doc: Toroid Class 12 Notes | EduRev

(iii) Impulse = change in momentum of the charge

= (-mv sin θ + mv cos θ Doc: Toroid Class 12 Notes | EduRev) - (mv sin θ Doc: Toroid Class 12 Notes | EduRev + mv cos θ ) = -2mv sinθDoc: Toroid Class 12 Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!
204 videos|288 docs|125 tests

< Previous

Dynamic Test

Content Category

Related Searches

Doc: Toroid Class 12 Notes | EduRev

,

mock tests for examination

,

practice quizzes

,

shortcuts and tricks

,

past year papers

,

MCQs

,

study material

,

pdf

,

Objective type Questions

,

Important questions

,

Exam

,

Previous Year Questions with Solutions

,

Viva Questions

,

ppt

,

Sample Paper

,

Doc: Toroid Class 12 Notes | EduRev

,

Free

,

Doc: Toroid Class 12 Notes | EduRev

,

Extra Questions

,

video lectures

,

Summary

,

Semester Notes

;