A charged particle having charge $$10-6$$ C and mass of $$10-10$$ kg is fired at the middle of the plate making an angle $$30$$° with plane of the plate. Length of the plate is $$0$$. $$17$$ m and it is separated by $$0.1$$ m. Electric field $$E=10-3$$ $$N/C$$ is present between the plates. Just outside the plates magnetic field is present. Find the magnitude of the magnetic field (in$$ $$mT)perpendicular$$ to the plane of the figure, if it has to graze the plate at C and A $$(in$$ $$mT) parallel to the surface of the plate.(Neglect$$ $$gravity)

Question

A charged particle having charge $$10-6$$ C and mass of $$10-10$$ kg is fired at the middle of the plate making an angle $$30$$° with plane of the plate. Length of the plate is $$0$$. $$17$$ m and it is separated by $$0.1$$ m. Electric field $$E=10-3$$ $$N/C$$ is present between the plates. Just outside the plates magnetic field is present. Find the magnitude of the magnetic field (in$$ $$mT)perpendicular$$ to the plane of the figure, if it has to graze the plate at C and A $$(in$$ $$mT) parallel to the surface of the plate.(Neglect$$ $$gravity)

Infinity Learn · Accepted Answer

To graze at CUsing equation of trajectory of parabola,$$y=xtan$$θ$$-ax22v2cos2$$θ          (i)  Here, $$a=qEm=10-6$$×$$10-310-10=10$$ $$m/s2$$ Substituting in equation (i), we have  $$0.05=0.17tan30$$°$$-10$$×$$(0.17)22v2$$×$$(3/2)2Solving$$ this equation, we have v $$-$$ $$2$$ $$m/sIn$$ magnetic field, AC $$-$$ Zror $$0.1$$ $$=$$ $$2ror$$ $$r=0.05m=mvcos30$$°Bq ∴  $$B=mvcos30$$°$$(0.05)q=10-10(2)(3/2)(0.05)10-6$$ $$=3.46$$×$$10-3$$ $$T=3.46mT$$

Motion of a charged particle

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