A magnetic field exists in the region and in the region where is a positive constant. A positive point charge moving with a velocity where is a positive constant, enters the magnetic field at . The trajectory of the charge in this region can be lik

Question

A magnetic field $\vec{B} = B_{0} \hat{j},$ exists in the region $a < x < 2 a$ and $\vec{B} = - B_{0} \hat{j},$ in the region $2 a < x < 3 a,$ where $B_{0}$ is a positive constant. A positive point charge moving with a velocity $\vec{v} = v_{0} \hat{i},$ where $v_{0}$ is a positive constant, enters the magnetic field at $x = a$ . The trajectory of the charge in this region can be like [2007]

Smart Achievers · Accepted Answer

(1)

Use the vector form of $\vec{B}$ and $\vec{v}$ in the formula $\vec{F} = q (\vec{v} \times \vec{B})$ to get the instantaneous direction of force at $x = a$ and $x = 2 a$ .

In the region $a < x < 2 a$ force must be in the direction $\hat{i} \times \hat{j}$ i.e., $+ z$ -direction, so vertically upward. And in the region $2 a < x < 3 a$ , in $- z$ -direction vertically downward.

Solution

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