The magnetic force acting on the proton is

where
q is the proton charge
v is its speed
B is the intensity of the magnetic field

is the angle between the direction of v and B; since the proton is moving perpendicular to the magnetic field,

and

, so the force becomes

this force provides the centripetal force that keeps the proton in circular motion:

where the term on the left is the centripetal force, with
m being the mass of the proton
r the radius of its orbit
Re-arranging the previous equation, we can find the radius of the proton's orbit:

And now we can calculate the centripetal acceleration of the proton, which is given by
Max ang. speed(u) = 18 rad/s
final ang. speed(v) = 0
ang. displacement(s) = 220 rad
ang. acceleration = (v^2 - u^2)/2s = -18^2 / 2*220 = -0.7364 rad/s^2
v = u +at
0 = 18 - 0.7364t
t = 18/0.7364
t = 24.44 seconds
Answer:
A)
B)
C)
Explanation:
Given that:
- no. of turns i the coil,

- area of the coil,

- time interval of rotation,

- intensity of magnetic field,

(A)
Initially the coil area is perpendicular to the magnetic field.
So, magnetic flux is given as:
..................................(1)
is the angle between the area vector and the magnetic field lines. Area vector is always perpendicular to the area given. In this case area vector is parallel to the magnetic field.


(B)
In this case the plane area is parallel to the magnetic field i.e. the area vector is perpendicular to the magnetic field.
∴ 
From eq. (1)


(C)
According to the Faraday's Law we have:



Answer:
C. Increasing its buoyancy