Question

Which one of the conditions can cause a particle to move with uniform circular motion in a uniform magnetic field

Answer 1

Given that,

A particle to move with uniform circular motion in a uniform magnetic field.

Suppose, The conditions are,

(I). The charged particle has to be positive and it should be moving in a direction opposite to a uniform magnetic field.

(II). The charged particle should be moving parallel to the magnetic force and perpendicular to the magnetic field.

(III). The magnetic field should be uniform and charge particle should be moving perpendicular to the magnetic field.

We know that,

An particle to move with uniform circular motion.

Here, electric force is perpendicular to velocity of particle.

The electric field is defined as,

`F_(c)=(mv^2)/(r)`.....(I)

Suppose, there is magnetic field, if a charge moving with velocity and the magnetic field exerts a field.

The magnetic force is defined as,

`F_(m)=qvB`.....(II)

We need to find the magnetic field

Using equation (I) and (II)

`F_(c)=F_(m)`

`(mv^2)/(r)=qvB`

`B=(mv)/(qr)`

Hence, The magnetic field should be uniform and charge particle should be moving perpendicular to the magnetic field.

(III) is correct option.