The next two questions pertain to the situation described below. A charged parti

Question

The next two questions pertain to the situation described below. A charged particle is accelerated through a potential difference from a to b. The then enters a uniform magnetic field B directed into the plane of the paper. While in magnetic field, the particle travels in a semicircle of diameter d. If we were to double the magnitude of the potential difference between a and b, what would happen to the diameter squareroot 2 d would double d would increase by a factor of d would stay the same Let T be the amount of time the particle is in the shaded region that contains the magnetic field. If we were to double the particle velocity as it enters the field, what would happen to T T would double T would increase by a factor of squareroot 2 T would stay the same

Explanation / Answer

14. suppose potential diff is V then

KE of particle after passing that PD = qV

m v^2 /2 = qV

v = sqrt(2qV/ m)

in magnetic field, charged particle will move in circular path,

Fm = mv^2 / r

q v B = mv^2 / r

r = m v / q B   = m sqrt(2qV/m) / qB = sqrt(2mV / q) / B

d = 2r = 2 sqrt(2mV / q) / B

now V is doubled then

d will become sqrt(2) times.

Ans (b)

15. r = m v / qB

and T = 2pi r / v   = 2 pi (m v / qB) / v   = 2pi m / qB

T is independent of speed of particle.

Ans(c)

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