Class 12th

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Explanation- considering magnetic field along B=Bk and electron enters with a velocity v=vi into a cubical region

The force on electron using Lorentz force = -e (vi $*$ Bk)= evBi

So the force F= -eE₀ k accelerates along z axis which in turn increases the radius of circular path and hence particle transversed on spiral path.

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

Explanation- general formula for magnetic field at center is

B= $\frac{{\mu }_{0}I}{4\pi r}\left(\theta \right)$

B1= $\frac{{\mu }_{0}I}{4\pi r}\left(\frac{\pi }{2}\right)=\frac{{\mu }_{0}I}{8r}$ k for xy plane

B2= $\frac{{\mu }_{0}I}{8r}$ i for zy plane

B3= $\frac{{\mu }_{0}I}{8r}$ j for xz plane

After joining together B= $\frac{{\mu }_{0}I}{8\pi r}$  (i+j+k)

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

Explanation – in biot savart law, magnetic field B is parallel to idlr and idl have its direction along the direction of flow of current.

Here, for the direction of magnetic field at O₂, due to wire carrying I₁ current is B| parallel idl $*$ r or I $*$ k, but it is -j

So the direction at O₂ is along y-direction.

The direction of magnetic force exerted at O2 because of the wire along x-axis

F= ilB=j (-j)=0

So the force is zero.

This is a short answer type question as classified in NCERT Exemplar

No, the potential function have no free space because when there is a free space there will be a leakage of potential at that point.

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

Explanation – here, the condition of magnetic resonance is violated.

When the frequency of radio frequency field were doubled, the time period of the radio frequency field were halved. Therefore, the duration in which particle completes half revolution inside the dees, radio frequency completes the cycle.

Hence, particle will accelerate and decelerate alternatively. So the radius of path in the dees will remain same.

This is a short answer type question as classified in NCERT Exemplar

It is only possible when their sizes are different . when their sizes are different there capacity would change. So there is potential difference btween them.

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

Explanation- yes, the magnetic force differ from inertial frame to frame. The magnetic force is frame dependent.

The net acceleration which comes into existing out of this is however, frame independent for inertial frames.