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(A) When a charged particle enters a uniform magnetic field perpendicularly,it follows a circular path. In the given figure,the particle enters the ma

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$2	heta$

Vedclass · Answer

(A) When a charged particle enters a uniform magnetic field perpendicularly,it follows a circular path. In the given figure,the particle enters the magnetic field region at an angle $	heta$ with the normal to the boundary. Due to the Lorentz force,the particle follows a circular arc within the magnetic field. By symmetry,the particle exits the magnetic field at the same angle $	heta$ with the normal to the boundary on the other side. The angle of deviation $\delta$ is the angle between the direction of the incident velocity vector and the direction of the emergent velocity vector. From the geometry of the path,the angle between the normal and the velocity vector at the entry point is $	heta$. The angle between the normal and the velocity vector at the exit point is also $	heta$. The total deviation $\delta$ is given by $\delta = 180^\circ - (90^\circ - 	heta) - (90^\circ - 	heta) = 2	heta$. Alternatively,as shown in the solution figure,the deviation angle $\delta$ is $2	heta$.

$A$ positively charged particle enters a region of a uniform transverse magnetic field as shown in the figure. Find the net deviation in the path of the particle.

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