The figure below shows a horizontal wire of infinite length that carries a const

Question

The figure below shows a horizontal wire of infinite length that carries a constant current of I = 30 A flowing to the right. Below the wire (a distance x from the wire) moves a very small particle of charge q with a speed of v = 6 × 106 m/s directly to the right.Below the horizontal wire is a constant electric field E = 1000 N/C pointing down the page. Determine the value of x if the motion of the charged particle is always to the right, parallel to the wire.

The figure below shows a horizontal wire of infinite length that carries a constant current of I 30 A flowing to the right. Below the wire (a distance r from the wire) moves a very small particle of charge q with a speed of v6 x 106 m/s directly to the right. he charge moves to the right and there is no gravity Below the horizontal wire is a constant electric field E 1000 N/C pointing down the page. Determine the value of x if the motion of the charged particle is always to the right, parallel to the wire.

Explanation / Answer

Electric field is downwards and magnetic field is upwards in the region where charge is moving. These are te only forces present, so they must balance each other.

So, magnetic force = electric force

So, qvB= qE

where q= charge, E= Electric field, B = magnetic field, v= velocity

So, vB= E

So, B= E/v = 1000 / 6*10^6 = 1.67*10^-4 T

Now, at distance x from wire, field is B = mu0*I/2*pi*x

where mu0= 1.25*10^-6 and I= 30A

So, B = 1.25*10^-6* 30 / 2*3.14*x

As the charge is moving at a distance x from wire, so, 1.25*10^-6* 30 / 2*3.14*x = 1.67*10^-4 T

So, x= 1.25*10^-6* 30 / 1.67*10^-4 T*2*3.14 = 0.03592m

So, the distance x is 0.03592m

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