Question

Constants In (Figure 1), a beam of protons moves through a uniform magnetic field with magnitude...

Constants

In (Figure 1), a beam of protons moves through a uniform magnetic field with magnitude 2.0 T , directed along the positive z axis. The protons have a velocity of magnitude 3.0×105 m/s in the x-z plane at an angle of 30 ∘ to the positive z axis. Find the force on a proton. The charge of the proton is q=+1.6×10−19C.

SOLUTION

SET UP We use the right-hand rule to find the direction of the force. The force acts along the y axis, so we curl the fingers of our right hand around this axis in the direction from v⃗  toward B⃗ . We find that the force acts in the −y direction.

SOLVE To find the magnitude of the force, use the magnetic force equation:

F===qvBsinϕ(1.6×10−19C)(3.0×105m/s)(2.0T)(sin30∘)4.8×10−14N.

REFLECT We could also obtain this result by finding B⊥ and applying F=|q|vB⊥. However, since we were given the angle ϕ, the equation we used is more convenient. To check for consistency of units, we recall that 1T=1N/(A⋅m).

Part A - Practice Problem:

An electron beam moves through a uniform magnetic field with magnitude 3.4 T , directed in the −z direction. The electrons have a velocity of 2.7×104 m/s in the y-z plane at an angle of 39 ∘ from the −z axis toward the +y axis. Find the force on an electron.

Express your answer to two significant figures and include appropriate units. Your answer should be positive if the force is in the +x direction and negative if the force is in the −x direction.

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