Question

1) An alpha particle is whizzing by at a velocity determined by its KE of 5 Mev.

a ) What is the velocity of the alpha particle?

b) What is the magnetic field at the position of a nucleus 2nm away from the alpha particle at angle of 900 to the velocity of the alpha. Alpha particle has a charge of 2e but a mass of 4 protons.

2) A long solenoid of 80 turns and length 16 cm is known to have a field of 4x10 ^-3 T. What is the current in the coil?

Answer 1

Q.1 Part A) We know that

K imena V = 2K m W = 2 x 5 x 1.6 x 10-13 J 4 x 1.67 x 10-28 kg v = 4.89 x 107 m/s

Part B) Magnetic field at the center is given by

$B = \frac{\mu_0 I}{2r}$

Where

$\\ I = \frac{q}{T} \\ \\ T = \frac{2 \pi r}{v} \\ \\ I = \frac{qv}{2\pi r}$

$B = \frac{ \mu_0 qv}{4\pi r^2}$

$B = \frac{ 4\pi \times 10^{-7} \ \rm T.mA^{-1} \times 2 \times 1.6 \times 10^{-19} \ \rm C \times 4.89 \times 10^{7}\ \rm m/s}{4\pi \times (2.0 \times10^{-9}\ \rm m)^2}$

$B = 0.39 \ \rm T$

Q.2. We know that

$\\ B = \mu_0 nI \\ \\ I = \frac{B}{\mu_0 n} \\ \\ I = \frac{BL}{\mu_0 N}$

As n = N/L

$\\ I = \frac{4 \times 10^{-3}\ \rm T \times 0.16 \ \rm m}{4 \pi \times 10^{-7}\ \rm T.mA^{-1} \times 80N} \\ \\ I = 6.37 \ \rm A$