An electron is accelerated through an electric potential of 173 V, then enters a

Question

An electron is accelerated through an electric potential of 173 V, then enters a 47 Gauss magnetic field in a direction at a right angle to the velocity. Find the radius in cm of the subsequent circular path for this electron. Express the answer with two decimal places.

The correct answer is 0.94. Please explain how to get to this answer.

An electron is accelerated through an electric potential of 173 V, then enters a 47 Gauss magnetic field in a direction at a right angle to the velocity. Find the radius in cm of the subsequent circular path for this electron. Express the answer with two decimal places.

The correct answer is 0.94. Please explain how to get to this answer.

Explanation / Answer

conserving energy,

0.5 mv^2=eV

or 0.5*9.1*10^-31*v^2=1.6*10^-19*173

or v=7.8*10^6 m/s

now magnetic field=47*10^-4 T

so balancing forces,

qVB=mv^2/r

1.6*10^-19*47*10^-4=(7.8*10^6)*9.1*10^-31/r

or r=9.44*10^-3 m

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