(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

when protons travelling north in a horizontal plane enter a region of uniform magnetic field of 0.8Teslas in the downward direction, they are deflected into a horizontal circle of radius 0.2 meters. what is the magnitude and direction of a uniform electric field applied over the same region of space that will allow the protons to pass through the region undelflected

2. Relevant equations

radius r = mv/qB where m is mass, v is velocity, q is charge, B is magnetic field

electromagnetic force F = qE + qv X B where X indicates cross product

electric field force F_E = qE where E is electric field

magnetic force F_B = qv X B where B is magnetic field

charge of electron/proton = 1.6*10^-19 coulombs

mass proton m = 1.67*10^-27 kg

3. The attempt at a solution

i used :

since the proton must not be deflected, i assumed electric field force must equal magnetic force so:

qE = qv X B

i then used radius eq, r = mv/qB and solved for v --> v = qBr/m and subbed it in for v to get:

qE = q(qBr/m) X B and solved for E --> E = (qBr/m)Bsin(theta), i have q = 1.6*10^-19 coulombs, B = 0.8 Teslas, r = 0.2 meters, mass m = 1.67*10^-27 kg but what is theta?

is my approach correct?

cheers

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# Electric field and magnetic field - proton deflection

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