A proton moves at 6.17 × 105 m/s undeflected in the + x direction through a velo

Question

A proton moves at 6.17 × 105 m/s undeflected in the +x direction through a velocity selector, a device containing crossed electric and magnetic fields. You measure the electric field to be2.0 × 105 N/C in the positive z direction.

A) Determine the magnitude of the magnetic field B .

B = ___________

B) Determine the direction of the magnetic field B .

a. in the positive z direction

b. in the positive x direction

c. in the negative z direction

d. in the negative x direction

e. in the positive y direction

f. in the negative y direction

c) If the proton's speed doubles, in which direction is it deflected?

a. in the positive z direction

b. in the positive x direction

c. in the negative z direction

d. in the negative x direction

e. in the positive y direction

f. in the negative y direction

Explanation / Answer

Taking +x as +i unit vector, +y as +j and +z as +k

Given:

Velocity of proton, v = 6.17x105 (+i) m/s

Electric field, E = 2x105 (+k) N/C

Solution:

a) If the proton is moving undeflected, that means the electric force and magnetic forces balance each other out

Felec = qE

Fmagn = qvXB

Equating the two forces gives us

qE = qvXB

E = vXB

Since the electric and magnetic fields are crossed i.e. perpendicular to each other, and the proton moves perpendicular to the electric field, it also moves perpendicular to the magnetic field.

Hence we have

|vXB| = vBsin90 = vB

So,

|E| = vB

B = |E| / v = 2x105 / 6.17x105 = 0.324 T

b) The direction of the magnetic field can be determined by looking at the direction of the magnetic force

Since the magnetic force acts opposite to electric force, it acts in negative z or -k unit vector

Velocity acts along +i unit vector

+i X B = -k

As +i X -j = -k

B acts in the -j or negative y direction

c) If the proton's speed doubles, the magnetic force doubles (qvB)

So the proton will be deflected in the direction of the magnetic force i,e, -k or negative z direction

Ans.

a) Magnitude of magnetic field is 0.324 T

b) f. Magnetic field acts along the negative y direction

c) c. The proton will get deflected in the negative z direction

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