A particle having a charge `q=1C` and mass `m=0.5kg` is projected on a rough horizontal plane `(x,y)` from a point `(15m,0,0)` with a initial velocity `vec(v)=20j`. In space a uniform electric field `vec(E)=25(-hat(k))` and magnetic filed `vec(B)=10(-hat(k))`. The acceleration due to gravity `g=10sec^(-2)` and co`-` efficient of friction `mu=0.5` . The particle moves on a spiral path and reaches to the origin . The time taken by particle to reach origin is found `yxx10sec`. Find `y`.

Answer

2

Explanation

`m(dv)/(dt)=-mu(mg+qE)`
`(mv^(2))/(r)=qvBimpliesr=(mv)/(qB)(dv)/(dt)=(qB)/(m)xx(dr)/(dt)`
`int_(0)^(t)dt=-(1)/(mu)" "int_(a)^(0)(qB)/(mg+qE)dr,impliest=20sec`
`B=(mu_(0)I)/(4piR)ln(sqrt(2)+1)impliesn=1`