(b) A neutron, a proton and an electron enter a uniform...

(b) A neutron, a proton and an electron enter a uniform magnetic field perpendicularly with the same speed. The paths of the three particles are as shown in the diagram. (i) Determine the path of each particle. (ii) Compare the speeds of the particles in the magnetic field. (iii) Which particle has the largest radius of circular path? Proton or electron? (iv) Find the ratio of the radii of the circular paths of electron and proton. (c) An electron enters a uniform electric field between two charged parallel plates of potential difference of 1000 V and 5.0 cm apart as shown in the diagram. The electron moves with a speed of $2.3 \times 10^7$ m s$^{-1}$ in a straight line perpendicular to a magnetic field with magnetic flux density B. Calculate the value of B.

Transcript

00:01 Hi guys, now in this long a proton moves through a uniform magnetic field where b is equal to this b is equal to 10 i cap minus 20 inch a cap minus 30 k cap mili tesla now at a time proton has a velocity v is equal to this is v x of i cap and this is v y of j cap and this is 20 this is 200 k cap meter per second magnetic force due to magnetic field f is equal to this is 4 times 10 to the power minus 17 i cap plus 2 times 10 to the power minus 17 this is j cap newton what will be this vx and vy we have a proton that discharge is equal to 1 .6 times 10 to the power minus of 19 coulomb we know that force f is equal to q times k ux cross b here what we have basically this is q this is q which means what 1 .6 times 10 to the power minus of 19 and here we have what this is 10 i cap sorry we have so this v of x i cap plus and this is v of y j cap and this is 200 we have a 10 to the power minus 3 as well this is a cross 10 i cap minus 20 is a cap minus 30 k cap times 10 to the power minus 3 so let me write down this i can say that this is 10 to part 22 because we have a military slizer so that is 10 to power minus 19 times 10 to the power minus 3 which means that 10 to the power minus 22 i can say that this f is equal to 4 so let me say in a different way 1 .6 sorry 4 divide by 1 .6 which means i can say this is 2 .5 times this will be 10 to the power 22 which means what this is 5 i cap plus now then we have 2 divide by 1 .6 which means what 1 .25 times 10 to the power 5 j cap okay now here v of x i cap gets equal this will be what v of x i cap times 10 i cap will be 0 this v is equal to what this v is equal to 20 ,000 sorry 2000 okay this v is equal to 2000 and then we have a k cap now this is minus 20 v x k cap and then we have a minus of 30 this is what minus 30 v of x i cap cross k cap which would work minus of j cap so that's it's positive j cap then we have a this is now from there what do you can say that now k cap is zero as you can see kker term is not available here so we can say simply that this 20 v of x is equal to minus of 10 v of y or i can say this is 2v of x is equal to minus of v of y one thing you can say here from this position what you can say this is i cap and from this will be what you can say that this is 2 .5 times this is 1 0000 and it will multiply it what this is 2 5 and then after we have a 4 0 okay so we have a 2 5 this will be 2 5 and then we have a this is 0 then we have a 4 0 0 0 and 0 is equal to this is 40 and then we have how many 0 that we have this is 3 0 this is 30 this is 30 of y of y of so from here v of y is equal to what? it will be this is minus of 7000 0 0...

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