Difficult to imagine!

A charged particle of mass m \displaystyle m and charge q \displaystyle q is released from the origin with a velocity v = v o i ^ \displaystyle \vec{v} = v_o \hat{i} in a uniform magnetic field B = B o 2 i ^ + 3 B o 2 j ^ \displaystyle \vec{B} = \frac{B_o}{2}\hat{i} + \frac{\sqrt{3}B_o}{2}\hat{j}

If R \displaystyle R represents the pitch (in meters) of the helical path described by the particle, the find the value of ( R 11 ) (R-11) to the nearest integer .

Details and Assumptions:
\bullet Consider a standard Right-handed Cartesian coordinate system.
\bullet m = 0.1 g \displaystyle m = 0.1g
\bullet q = 10 μ C \displaystyle q = 10\mu C
\bullet v o = 20 m / s \displaystyle v_o = 20 m/s
\bullet B o = 8 T \displaystyle B_o = 8 T


The answer is 68.

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1 solution

Arghyanil Dey
Apr 26, 2014

The velocity vector makes an angle 60° with the given magnetic field.

The pitch of the helix is = 2 π m v cos θ ÷ q B = 78.5 2πmv\cos\theta÷qB=78.5

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