Two charges of same magnitude move in two cir | vedclass

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Question

(A) The magnetic force $F$ on a charged particle moving with velocity $v$ in a magnetic field $B$ is given by the Lorentz force formula: $F = q(v 	im

Vedclass · Accepted Answer

$W_1=W_2=0$

Vedclass · Answer

(A) The magnetic force $F$ on a charged particle moving with velocity $v$ in a magnetic field $B$ is given by the Lorentz force formula: $F = q(v 	imes B)$.Since the force $F$ is the cross product of $v$ and $B$,it is always perpendicular to the velocity vector $v$.The work done $W$ by a force over a displacement $ds$ is given by $W = \int F \cdot ds$. Since $ds = v dt$,we have $W = \int (F \cdot v) dt$.Because $F$ is perpendicular to $v$,the dot product $F \cdot v = 0$ at all times.Therefore,the work done by the magnetic field on a moving charged particle is always zero,regardless of the radius of the circular path.Hence,$W_1 = W_2 = 0$.

Two charges of same magnitude move in two circles of radii $R_1=R$ and $R_2=2R$ in a region of constant uniform magnetic field $B_0$. The work $W_1$ and $W_2$ done by the magnetic field in the two cases respectively,are such that

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