IIT-JEE 2012 · Paper 1 · Physics Q14

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PhysicsMultiple correct+4Question 14 of 60

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 $t>0$ ?

\theta=0°

, the charge moves in a circular path in the

x

z

plane.

\theta=0°

, the charge undergoes helical motion with constant pitch along the

y

-axis.

\theta=10°

, the charge undergoes helical motion with its pitch increasing with time, along the

y

-axis.

\theta=90°

, the charge undergoes linear but accelerated motion along the

y

-axis.

Answer and worked solution

Official answer: C, D

Both fields are along $\hat j$ . The magnetic force acts only on the velocity component perpendicular to $y$ (circular motion in the $x$ - $z$ plane); the electric force accelerates the charge uniformly along $y$ .

(A) For $\theta=0$ the charge circles in the $x$ - $z$ plane while also accelerating along $y$ , so the path is not confined to that plane. False.
(B) The $y$ -velocity grows, so the pitch is not constant. False.
(C) For $\theta=10°$ : a helix about the $y$ axis whose pitch increases as $v_y$ grows. True.
(D) For $\theta=90°$ the velocity is along $\vec B$ , so there is no magnetic force; $\vec E$ accelerates it along $y$ : straight-line accelerated motion. True.

(C), (D)

Topics:Motion in magnetic and electric fields Force on a moving charge

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IIT-JEE 2012 · Paper 1, Physics question 14