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Standard XII

Physics

Current Loop Is a Magnet?

A proton is m...

Question

A proton is moving in a gravity free space having a uniform electric field $E$ of unknown magnitude and direction. There is a uniform magnetic field of $0.01 T$ pointing in the $y$ - direction. The proton moves in the $x$ - direction at a constant velocity of $10 km/s$ . All directions are with respect to the usual right handed $x - y - z$ coordinate system. Which of the following is /are correct ?

E_{z} = 100 V/m

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E_{z} = - 100 V/m

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E_{y} = 100 V/m

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E_{x} = 0 V/m

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Solution

The correct option is D $E_{x} = 0 V/m$

Using Lorentz equation, ${\to F}_{n e t} = - e \to E + - e [\to V \times \to B]$

In this case , ${\to F}_{n e t} = 0$

$\Rightarrow \to E = - \to v \times \to B = - (10, 000^i \times 0.01^j)$

$\Rightarrow \to E = - 100^k$

$\Rightarrow {¯ E}_{x} = 0; E_{y} = 0; E_{z} = - 100$

Hence, options (b) and (d) are the correct answers.

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The correct option is D Ex=0 V/m Using Lorentz equation, →Fnet=−e→E+−e[→V×→B] In this case , →Fnet=0 ⇒→E=−→v×→B=−(10,000^i×0.01^j) ⇒→E=−100^k ⇒¯Ex=0 ; Ey=0 ; Ez=−100 Hence, options (b) and (d) are the correct answers.