A particle having a charge of 5.0 μC and a mass of 5.0 × 10–12 kg is projected with a speed of 1.0 km s–1 in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin–1(0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.

Given-
Charge on the particle, q = 5 μC = 5 × 10−6 C

Magnetic field, B = 5 × 10−3 T

Mass of the particle, m = 5 × 10−12 kg

Velocity of projection, v = 1 Km/s = 103 m/s

Angle between the magnetic field and velocity,

θ= sin−1(0.9)

Since there are no forces in the horizontal direction ie there is no force in the direction of magnetic field, so, the particle moves with uniform velocity in horizontal direction.

Thus, it moves in a helical form.In helical motion we have two components of velocity.

Component of velocity which is perpendicular to the magnetic field is given by -

Similarly component of velocity in the direction of magnetic field will be the parallel component given by -

The velocity has a vertical component along which it accelerates with an acceleration a and moves in a circular cross-section.

We know motion in helical direction which is centripetal force and is given by –

Now, this force is balanced by Lorentz force acting due to presence of magnetic field ,

Hence, diameter of the helix can be calculated as ,

And the Pitch of the helix is ,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Equation of electric and magnetic field52 mins
Magnetic force on moving charge particle in magnetic field | Quiz32 mins
Magnetic force on moving charge particle in magnetic field44 mins
Magnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loop36 mins
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Few Applications of Gauss's law54 mins
Electric field inside cavity37 mins
Gain Confidence on Magnetic Effects of Current with Questions41 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses