Magnetic fields are often used to measure the mass of very small particles. The

Question

Magnetic fields are often used to measure the mass of very small particles. The diagram at right (It's a circle with arrows pointing towards counterclockwise) indicates the path of an electron moving in a magnetic field of 320 mT perpendicular to the plane of the page.

a) If the electron is moving with a velocity of 6.1 x 10^4 m/s, calculate the mass of the electron assuming the diagram is drawn full scale.

b) Is the magnetic field coming out of the paper or going into the paper? Explain.

c) If the electron had twice the mass, would its path have a small or greater diameter? Explain.

Explanation / Answer

Since you have not indicated the radius of the path I will simply give equations to help you out. (I believe you need the radius) (a) Since F = q(v x B) = qvBsin(phi) = qvB let F = ma = m(v^2)/r [centripetal force] equating the two: m = (q*r*B)/v [q is electron charge, r is radius] ......(1) (b) Using a right hand rule of F = q(v x B). Let us note that the charge is negative so the force we use for the right hand rule we need it to be opposite. That being said point your hand towards velocity (counterclockwise) and cross it out of the page (towards you) your thumb points up indicating a upward force. Since our charge is negative the force is inverted meaning the force is towards the center which is what we want (centripetal force). This means that the magnetic field is point out of the page, or towards you. (c) Take a look at equation (1). If everything else is constant and we doubled the mass, the right hand side of the equation would have to counter-balance it meaning that r (radius) would increase. Therefore the diameter would increase.

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