Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_{0} \hat{j}$ and $\vec{B}=B_{0} \hat{j}$. At time $t=0$, this charge has velocity $\vec{v}$ in the $x-y$ plane, making an angle $\theta$ with the $x$-axis. Which of the following option(s) is(are) correct for time $t>0$ ?

(C) If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.; (D) If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.

(A) If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.

(B) If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.

JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Magnetic Effects of Current

WhatsApp Email

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields

E = E_{0} \hat{j}

and

B = B_{0} \hat{j}

. At time

t = 0

, this charge has velocity

v

in the

x - y

plane, making an angle

θ

with the

x

-axis. Which of the following option(s) is(are) correct for time

t > 0

(A)If $θ = 0^{\circ}$ , the charge moves in a circular path in the $x - z$ plane.
(B)If $θ = 0^{\circ}$ , the charge undergoes helical motion with constant pitch along the $y$ -axis.
(C)If $θ = 1 0^{\circ}$ , the charge undergoes helical motion with its pitch increasing with time, along the $y$ -axis.✓ Correct
(D)If $θ = 9 0^{\circ}$ , the charge undergoes linear but accelerated motion along the $y$ -axis.✓ Correct

Answer: (C), (D)

Solution

When

θ = 9 0^{\circ}

v

is along

\hat{j}

, parallel to both

E

and

B

. The magnetic force is zero, and the electric force accelerates the charge linearly along

y

. When

θ = 0^{\circ}

1 0^{\circ}

, the velocity has a component perpendicular to

B

, causing circular motion in the

x - z

plane, while

E

accelerates it along

y

, resulting in helical motion with increasing pitch. Options (C) and (D) are correct.

JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · One or more correct options

Practise more: all JEE Advanced PYQs on Magnetic Effects of Current →

JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Magnetic Effects of Current

Solution

More JEE Advanced questions on Magnetic Effects of Current