A particle of charge q and mass m starts moving from the origin under the action of an electric field E→$$=E0i^$$ and B→$$=B0i^$$ with a velocity v→$$=v0$$ $$j^$$. The speed of the particle will be become $$3v0$$ after a time

Question

A particle of charge q and mass m starts moving from the origin under the action of an electric field E→$$=E0i^$$ and B→$$=B0i^$$ with a velocity  v→$$=v0$$ $$j^$$. The speed of the particle will be become $$3v0$$ after a time

Infinity Learn · Accepted Answer

E→ is parallel to B→ and v→ is perpendicular to both. Therefore, path of the particle is a helix with increasing pitch. Speed of particle at any time t is $$v=vx2+vy2+vz2Here$$,  in yz plane speed will remain same. Therefore,  $$vy2+vz2=v02Given$$ :  $$v=3v0v=vx2+vy2+vz2$$ ⇒$$v2$$ $$=$$ $$vx2+vy2+vz2$$ ⇒$$(3vo)2$$ $$=$$ $$vx2$$ $$+$$ $$vo2$$ ⇒$$vx2$$ $$=$$ $$8vo2$$ ⇒vx $$=$$ $$22vo$$ Equation of Kinematics, along x axis $$vx=ux+axt$$ ⇒$$22v0=0+qEmt$$ ⇒$$t=(22)mv0qE$$.

A particle of charge q and mass m starts moving from the origin under the action of an electric field $\vec{E} = E_{0} \hat{i}$ and $\vec{B} = B_{0} \hat{i}$ with a velocity $\vec{v} = v_{0} \hat{j}$ . The speed of the particle will be become $3 v_{0}$ after a time

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A particle of charge q and mass m starts moving from the origin under the action of an electric field E→=E0i^ and B→=B0i^ with a velocity v→=v0 j^. The speed of the particle will be become 3v0 after a time

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A particle of charge q and mass m starts moving from the origin under the action of an electric field $\vec{E} = E_{0} \hat{i}$ and $\vec{B} = B_{0} \hat{i}$ with a velocity $\vec{v} = v_{0} \hat{j}$ . The speed of the particle will be become $3 v_{0}$ after a time