A charged particle (electron or proton) is introduced at the origin (x

A charged particle (electron or proton) is introduced at the origin (x=0,y=0,x=0) with a given initial velocity →v. A uniform electric field →E and a uniform magnetic field →B exist everywhere. The velocity →v, electric field →E and magnetic field →B are given in column 1,2 and 3, respectively. The quantities E0, B0 are positive in magnitude.Column 1Column 2Column 3(I) Electron with →v=2E0B0^x(i) →E=E0^z(P) →B=−B0^x(II) Electron with →v=E0B0^y(ii) →E=−E0^y(Q) →B=−B0^x(III) Electron with →v=0(iii) →E=−E0^x(R) →B=B0^y(IV) Electron with →v=2E0B0^x(iv) →E=E0^x(S) →B=B0^z In which case will the particle move in a straight line with constant velocity?

Answer»

A charged particle (electron or proton) is introduced at the origin $(x = 0, y = 0, x = 0)$ with a given initial velocity $\to v$ . A uniform electric field $\to E$ and a uniform magnetic field $\to B$ exist everywhere. The velocity $\to v$ , electric field $\to E$ and magnetic field $\to B$ are given in column $1, 2$ and $3,$ respectively. The quantities $E_{0}, B_{0}$ are positive in magnitude.

Column 1	Column 2	Column 3
$(I)$ Electron with $\to v = 2 \frac{E_{0}}{B_{0}}^x$	$(i)$ $\to E = E_{0}^z$	$(P)$ $\to B = - B_{0}^x$
$(I I)$ Electron with $\to v = \frac{E_{0}}{B_{0}}^y$	$(i i)$ $\to E = - E_{0}^y$	$(Q)$ $\to B = - B_{0}^x$
$(I I I)$ Electron with $\to v = 0$	$(i i i)$ $\to E = - E_{0}^x$	$(R)$ $\to B = B_{0}^y$
$(I V)$ Electron with $\to v = 2 \frac{E_{0}}{B_{0}}^x$	$(i v)$ $\to E = E_{0}^x$	$(S)$ $\to B = B_{0}^z$

In which case will the particle move in a straight line with constant velocity?

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