One coulomb of point charge moving with a uniform velocity 10x^{⋀} m/s enters the region x ≥ 0 having a magnetic flux density B^{\to}=(10yx^{⋀}+10xy^{⋀}+10z^{⋀})T. The magnitude of force on the charge at x=0^{+} is ________ N.(x^{⋀},y^{⋀}) and z^{⋀} are unit vectors along x-axis, y-axis, and z-axis, respectively)

GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 42 of 65

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One coulomb of point charge moving with a uniform velocity

10x↖{⋀}

m/s enters the region x ≥ 0 having a magnetic flux density

B↖{→}=(10yx↖{⋀}+10xy↖{⋀}+10z↖{⋀})

T. The magnitude of force on the charge at

x=0^{+}

is ________ N.

(x↖{⋀},y↖{⋀})

and

z↖{⋀}

are unit vectors along x-axis, y-axis, and z-axis, respectively)

Solution:

{f}= {Q}( {v} × {B})=10[ {a}_{ {x}} ×(10 {ya}_{ {x}}+10 {xa}_{ {y}}+10 {a}_{ {z}})]

{F}=[10 {xa}_{ {z}}-10 {a}_{ {y}}] 10

{x}=0

{F}=[10 {a}_{ {y}}] 10

| {F}|=100 {N}

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