JEE MAIN - Physics (2021 - 25th February Morning Shift - No. 1)
A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.
2 : 1 : 1 and 4 : 2 : 1
4 : 2 : 1 and 2 : 1 : 1
1 : 2 : 4 and 2 : 1 : 1
1 : 2 : 4 and 1 : 1 : 2
Explicació
F = qvB = q$${p \over m}$$B
F $$ \propto $$ $${q \over m}$$ [as p, B are const.]
$$ \therefore $$ F1 : F2 : F3
= $${e \over m}:{e \over {2m}}:{{2e} \over {4m}}$$
= 2 : 1 : 1
And v1 : v2 : v3
= $${p \over m}:{p \over {2m}}:{p \over {4m}}$$
= 4 : 2 : 1
F $$ \propto $$ $${q \over m}$$ [as p, B are const.]
$$ \therefore $$ F1 : F2 : F3
= $${e \over m}:{e \over {2m}}:{{2e} \over {4m}}$$
= 2 : 1 : 1
And v1 : v2 : v3
= $${p \over m}:{p \over {2m}}:{p \over {4m}}$$
= 4 : 2 : 1