Question

A steady current flows through an infinitely long straight current
carrying conductor. A proton is projected with a velocity u in a
direction perpendicular to the plane containing the conductor as
shown, then

A)magnetic force on the proton is always zero

B)Initial magnetic force acting on the proton is towards right

C)Initial magnetic force acting on the proton is zero and proton moves along a straight path

D)Initial magnetic force acting on the proton is zero and it moves along a curved path.

Pls provide an explanation/reason for your answer.​

Answer 1

Given:

A steady current flows through an infinitely long straight current carrying conductor. A proton is projected with a velocity u in a direction perpendicular to the plane containing the conductor.

To find:

Correct option ?

Calculation:

First of all, let's find out the direction and magnitude of magnetic field intensity due to the wire at the location of the proton :

• Use RIGHT-HAND THUMB RULE.

$\therefore \: \vec{B} = \dfrac{ \mu_{0} \lambda}{2\pi r} ( - \hat{k})$

Now, velocity vector of proton :

$\therefore \: \vec{v} = v( - \hat{k})$

Now, force on proton will be :

$\therefore \: \vec{F} = q \: ( \vec{v} \times \vec{B})$

$\implies \: \vec{F} = q \: \bigg \{ v( - \hat{k}) \times \dfrac{ \mu_{0} \lambda}{2\pi r}( - \hat{k} ) \bigg \}$

$\implies \: \vec{F} = q \times 0$

$\implies \: \vec{F} = 0$

So, proton experiences zero magnetic force and always moves along a straight line .