An alpha-particle (m = 6.64 × 10−27 kg, q = 3.2 × 10−19 C) travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. What is the speed of the particle?

The speed of the particle is .

Explanation:

Given:

Mass of the alpha-particle (m) = 6.64 × 10⁻²⁷ kg

Charge of the particle (q) = 3.2 × 10⁻¹⁹ C

Magnitude of magnetic field (B) = 1.5 T

Radius of the circular path (r) = 25 cm = 0.25 m [1 cm = 0.01 m]

Speed of the particle (v) = ?

We know that, when a charged particle enters a uniform magnetic field, the path traced by the charged particle is circular and the radius of the circular path is given by the formula:

Expressing the above formula in terms of 'v', we get:

Now, plug in the values given and solve for 'v'. This gives,

Therefore, the speed of the particle is .

C. Africa

Explanation:

The data given on the graph shows that:

Asia will grow from around 1,300 million to 5,000 million in 2050 which is an increase of:

= 5,000 /1,300 = 3.84 times

Europe will decrease over that period.

Africa will go from around 300 million to 2,000 million which is an increase of:

= 2,000 / 300

= 6.67 times

Mexico

, Central America, Caribbean Islands:

= 900 / 120

= 7.5 times

United States,  Canada, and Greenland:

= 400/120

= 3.33

Oceania:

= 50 / 13

= 3.85

From the options give, Africa will see the greatest increase at 6.67 times its population in 1950.