Seema's uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it.
When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.
Based on the above paragraph, answer the question.
Assuming that MRI test was performed using a magnetic field of 0.1 T, find the minimum and maximum values of the force that the magnetic field could exert on a proton moving with a speed of $10^{4}$ m/s.
Given charge of proton = $1.6 \times 10^{- 19}$ C

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Solution

Force experienced by proton $\to F = q (\to v \times \to B)$
$∣ ∣ \to F ∣ ∣ = q v B s i n θ$
Maximum force ${∣ ∣ \to F ∣ ∣}_{m a x} = q v B$
$= 1.6 \times 10^{- 19} \times 10^{4} \times 0.1$
$= 1.6 \times 10^{- 16} N$
${∣ ∣ \to F ∣ ∣}_{m i n} = 0 N$

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Force experienced by proton →F=q(→v×→B)∣∣→F∣∣=qvBsinθMaximum force ∣∣→F∣∣max=qvB=1.6×10−19×104×0.1=1.6×10−16N∣∣→F∣∣min=0N

Force experienced by proton $\to F = q (\to v \times \to B)$
$∣ ∣ \to F ∣ ∣ = q v B s i n θ$
Maximum force ${∣ ∣ \to F ∣ ∣}_{m a x} = q v B$
$= 1.6 \times 10^{- 19} \times 10^{4} \times 0.1$
$= 1.6 \times 10^{- 16} N$
${∣ ∣ \to F ∣ ∣}_{m i n} = 0 N$