A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible?
(a) E = 0, B = 0
(b) E = 0, B ≠ 0
(c) E ≠ 0, B = 0
(d) E ≠ 0, B ≠ 0

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Solution

(a) E = 0, B = 0
(b) E = 0, B ≠ 0
(d) E ≠ 0, B ≠ 0

A charged particle can move in a gravity-free space without any change in velocity in the following three ways:

(1) E = 0, B = 0, i.e. no force is acting on the particle and hence, it moves with a constant velocity.

(2) E = 0, B ≠ 0. If magnetic field is along the direction of the velocity v, then the force acting on the charged particle will be zero, as F = q v $\times$ B = 0. Hence, the particle will not accelerate.

(3) If the force due to magnetic field and the force due to electric field counterbalance each other, then the net force acting on the particle will be zero and hence, the particle will move with a constant velocity.

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Q. A charged particle moves along a circle under the action of possible constant electric and magnetic fields. Which of the following is possible?
(a) E = 0, B = 0
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Q. A proton moving with a constant speed passes through a region of space without any change in its speed. If

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B \neq 0, E = 0

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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?

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) $\to B = - B_{0}^x$
(II) Electron with $\to v = \frac{E_{0}}{B_{0}}^y$	(ii) $\to E = - E_{0}^y$	(Q) $\to B = - B_{0}^x$
(III) Electron with $\to v = 0$	(iii) $\to E = - E_{0}^x$	(R) $\to B = B_{0}^y$
(IV) Electron with $\to v = 2 \frac{E_{0}}{B_{0}}^x$	(iv) $\to E = E_{0}^x$	(S) $\to B = B_{0}^z$

In which case would the particle move in a straight line along the negative direction of

y

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-^y) ?

Let a and b be nonzero real roots of the quadratic equation x²+ ax + b = 0 and a + b, a -b and - a -b be the roots of the equation x⁴+ax³+cx²+dx+e=0. Then which of the following statement is false?

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A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible? (a) E = 0, B = 0 (b) E = 0, B ≠ 0 (c) E ≠ 0, B = 0 (d) E ≠ 0, B ≠ 0

A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible?
(a) E = 0, B = 0
(b) E = 0, B ≠ 0
(c) E ≠ 0, B = 0
(d) E ≠ 0, B ≠ 0