A particle enters a space where a uniform magnetic field B = B x i ^ + B y j ^ + B z k ^ and a uniform electric field E = E x i ^ + E y j ^ + E z k ^ exist, with initial velocity u = u

Question

A particle enters a space where a uniform magnetic field $B = B_{x} \hat{i} + B_{y} \hat{j} + B_{z} \hat{k}$ and a uniform electric field $E = E_{x} \hat{i} + E_{y} \hat{j} + E_{z} \hat{k}$ exist, with initial velocity $u = u_{x} \hat{i} + u_{y} \hat{j} + u_{z} \hat{k}$ . Depending on the values of the components the particle selects a path. Match List-I with List-II. The components other than specified in List-I in each entry are non-zero. Neglect gravity.

List - I	List - II
(P) $B_{y} = B_{z} = E_{x} = E_{z} = 0, u = 0$	(1) circle
(Q) $E = 0, u_{x} B_{x} + u_{y} B_{y} \neq = - u_{z} B_{z}$	(2) helix with uniform pitch and constant radius
(R) $u \times B = 0, u \times E = 0$	(3) cycloid
(S) $u ⊥ B, u ⊥ E$	(4) helix with variable pitch and constant radius
	(5) straight line

TestHub · Accepted Answer

(P) Only B x ​ and E y ​ with u = 0: the drift gives a helix with variable pitch and constant radius, P → 4 . (Q) E = 0 and u ⋅ B  = 0 : uniform helix, Q → 2 . (R) u parallel to both fields: no magnetic force effect on direction, straight line, R → 5 . (S) u ⊥ B , u ⊥ E : helix with variable pitch and constant radius, S → 4 . Option (A).

Physics - Magnetism Question with Solution | TestHub

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