Question

In: Physics

A beam of photons (q = +1.6 x 10^-19 C) is moving with various speeds in...

A beam of photons (q = +1.6 x 10^-19 C) is moving with various speeds in the positive x direction (to the right). It enters a region where there is a uniform magnetic field of magnitude 0.25T pointing in the negative z direction (into the page).

a) The protons feel a force due to this magnetic field. Explain why, and indicate the direction of the force.

b) Not all protons will feel a force of the same magnitude. Why?

c) As a result of the magnetic force, the protons will deviate from their speed original direction towards the right. It is desired that those protons traveling at a speed of 1.75*10^5 m/s don't deviate at all and continue on a straight path to the right. This is to be achieved by turning on an electric field in the same region as the magnetic field. In what direction should the electric field point? Explain.

d) Find the magnitude of the electric field necessary to achieve the result of the previous question.

Expert Solution

a) A charge particle, moving in magnetic field, such that it's velocity not making an angle 0 or 180 deg with magnetic field, experience force.

As protons (moving along +ve x axis) velocity makes an angle of 90 deg with magnetic field ( -ve z axis), protons feel force.

Direction of force is given by direction of v×B .

x × (-z) is along + ve y direction. Hence force is towards+ve y direction.

b) magnitude of force on charge by magnetic field

= qvB sin(theta)

q is charge, v speed of charge particle, B is magnitude of magnetic field and theta is angle between velocity and magnetic field.

As this force depends upon speed of charge particle, Protons moving at different speeds, feel different force.

c) Force of electric field on proton should be equal and opposite to direction of magnetic force. Force on +ve charges due to electric field is in the direction of field.

To oppose force of magnetic field , electric field should be towards, - ve y axis.

d Magnitude of electric field = vb sin(theta)

= 1.75×10^5 m/s * 0.25 T * sin(90)= 4.4×10^4 N/C

genius_generous answered 4 months ago

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