Physics

This is a Long Answer Type Questions as classified in NCERT Exemplar

Explanation- the magnetic field induction at a pojnt z distance from dipole moment is

B= $\frac{{\mu }_o}{4\pi }\frac{2M}{z^3}$

Along z axis from p to q

${\int }_p^{Q}B.dl={\int }_P^{Q}Bdlcos0$ = ${\int }_P^{Q}Bdz$

= ${\int }_a^R\frac{{\mu }_o}{2\pi }\frac{M}{z^3}dz=\frac{{\mu }_{o}M}{2\pi }\left(-\frac{1}{2}\right)\left(\frac{1}{R^2}-\frac{1}{a^2}\right)$

= $\frac{{\mu }_{o}M}{4\pi }\left(\frac{1}{a^2}-\frac{1}{R^2}\right)$

(b) the point A lies on the equatorial line of the magnetic dipole of moment Msin $\theta$

B= $\frac{{\mu }_0}{4\pi }\frac{Msin\theta }{R^3}$ dl= Rd $\theta$

$\int B.dl=\int Bdlcos\theta ={\int }_0^{\frac{\pi }{2}}\frac{{\mu }_0}{4\pi }\frac{Msin\theta }{R^3}Rd\theta$

Circular arc = $\frac{{\mu }_o}{4\pi }\frac{M}{R}(-cos\theta )$ = $\frac{{\mu }_o}{4\pi }\frac{M}{R^2}$

(c) along x axis over the path ST

From figure every point lies on the equatorial line of magnetic dipole so

B= $\frac{{\mu }_o}{4\pi }\frac{M}{x^3}$   the value of B is zero as the angle between M and dl is 90 

(d)along the quarter circle TP of radius a

B along circular arc $\int B.dl={\int }_{\pi /2}^0\frac{{\mu }_0}{4\pi }\frac{Msin\theta }{a^3}$ d $\theta$

B = $-\frac{{\mu }_o}{4\pi }\frac{M}{a^2}$

Net magnetic field through PQST  is zero

This is a Multiple Choice Questions as classified in NCERT Exemplar

Explanation- for a charge particle to move in circular path

Mv²/r = qvB

v/r=w= bq/m

w= v/r = $\frac{L{T}^{-1}}{L}$ = T-1

This is a Multiple Choice Questions as classified in NCERT Exemplar

Explanation- force on charge particle due to both electric and magnetic field . now if electric force and magnetic field is zero then electric field and magnetic field is also zero.

Magnetic field is only responsible for constant velocity of charge particle if B=0 then E =0 if B is not equal to zero then electric field is also not equal to zero

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (b, c, d)

Explanation- magnetic forces on both the particles cause equal acceleration because they both have equal velocity

Also they both gain or loose energy because direction of force in both cases is opposite.

And there is no change in center of mass of particles so it is determined by B alone.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (b, c)

Explanation- if current is in opposite sense the? Bdl = 0, also there exist a point where b and dl is perpendicular.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (b, d)

Explanation- F=IlB, the direction of force is given by fleming's left hand rule and F is perpendicular to the direction of magnetic field. So work done is zero.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer – (a)

Explanation- gyro magnetic ratio does not depend upon which electron is rotating.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer. (d)

Explanation- W=MBcos $\theta$ , as the loop make 30 degree angle but angle made by axis of the loop with the direction of magnetic field, therefore work done is zero.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer – (a)

Explanation – when a charge particle enter in cyclotron it will always accelerated with the help of oscillating electric field. But it will move with the same speed with the help of magnetic field.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (d)

Explanation- when electron move in the direction of velocity along the axis of current then angle is 180 which makes force according to the relation F=qvbsin $?$ . so electron will continue move with uniform velocity along axis of solenoid.