Question

# An electron enters a uniform magnetic field B= 0.23T at a 45 degree angle to B. Determine the pitch p (distance between loops) of the electron's helical path assuming its speed to be 3.0\cdot10^6 m/s.

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An electron enters a uniform magnetic field B= 0.23T at a 45 degree angle to B. Determine the pitch p (distance between loops) of the electron's helical path assuming its speed to be $$\displaystyle{3.0}\cdot{10}^{{6}}$$ m/s.

2021-02-12
Given
magnetic field B = 0.23 T
angle $$\displaystyle\theta={45}$$
velocity $$\displaystyle{V}={3}\cdot{10}^{{6}}$$ m/s
time period of revolution
$$\displaystyle{T}={\frac{{{2}\theta{m}}}{{{B}{q}}}}$$
mass of the electron $$\displaystyle{m}={9.1}\cdot{10}^{{-{31}}}$$ kg
charge of the electron $$\displaystyle{q}={1.6}\cdot{10}^{{-{16}}}$$ C
$$\displaystyle\text{pitch of the helix}=\text{time period}\cdot\text{velocity(parallel)}$$
$$\displaystyle{V}_{{{p}{a}{r}{a}{l}\le{l}}}={V}\cdot{\cos{{45}}}$$