Chapter 20, Problem 11P

To determine

Magnetic field which is required to bend an alpha particle into a circular path of radius r = 0.14m.

Answer to Problem 11P

Solution:

Magnetic field $B=23.57\times {10}^{-2}$ T

Explanation of Solution

Given:

Charge q = +2e; mass m = $6.6\times {10}^{-27}$ kg; velocity $v=1.6\times {10}^6$ m/s; radius r =0.14m

Formula used:

$r=\frac{mv}{qB}$

Calculation:

For calculating the value of magnetic field we use the expression,

$r=\frac{mv}{qB}$

$r=\frac{mv}{2eB}$

$B=\frac{mv}{2er}$

$B=\frac{6.6\times {10}^{-27}\times 1.6\times {10}^6}{2\times 1.6\times {10}^{-19}\times 0.14}$

$B=23.57\times {10}^{-2}$ T