A proton is initially at rest and moves through three different regions as shown

Question

A proton is initially at rest and moves through three different regions as shown in the figure. In region 1, the proton accelerates across a potential difference of 3230 V. In region 2, there is a magnetic field of 1.10 T pointing out of the page and an electric field pointing perpendicular to the magnetic field and perpendicular to the proton's velocity. Finally, in region 3, there is no electric field, but just a 1.10 T magnetic field pointing out of the page.

(a) What is the speed of the proton as it leaves region 1 and enters region 2?
m/s

(b) If the proton travels in a straight line through region 2, what is the magnitude and direction of the electric field?

Explanation / Answer

a)

Here ,V = 3230 V

using work energy theroum

KE = work done by electric field

0.5*mp*u^2 = 3230*e

u = 7.87 * 10^5 m/s

speed of proton is 7.87 * 10^5 m/s

b)

For proton to go undeflected,

E = v*B

E = 7.87 * 10^5 * 1.1

E = 8.65 * 10^5 V/m

the magnitude of electric field is 8.65 * 10^5 V/m

and it is directed UPWARDS

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