QJEEM17Ph030b: JEE Main 2017 Physics - Class 12 JEEM17Ph030b Solution: In a certain region static electric and magnetic fields exist.…

Question

Verified Solution • 2025–26 Session moderate

In a certain region static electric and magnetic fields exist. The magnetic field is given by

\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)

. If a test charge moving with a velocity

\overrightarrow \upsilon = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right)

experiences no force in that region, then the electric field in the region, in SI units, is :

A $\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {3\widehat i - 2\widehat j - 4\widehat k} \right)$
B $\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {\widehat i + \widehat j + 7\widehat k} \right)$
C $\overrightarrow E = {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$
D $\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$

Accepted Answer

Here test charge experience no net force, So, sum of electric and magnetic field is zero.

\therefore\,\,\,

F_e + F_m = 0

\therefore\,\,\,

F_e =

-

q (

\overrightarrow v

\times

\overrightarrow B)

=

-

qB₀

\upsilon

₀ [(3

\widehat i

-

\widehat j

+ 2

\widehat k

)

\times

(

\widehat i

+ 2

\widehat j

-

4

\widehat k

)]

=

-

q

\upsilon

₀ B₀ (14

\widehat j

+ 7

\widehat k

)

Electric field produced by the charge q,

\overrightarrow E

=

{{\overrightarrow {{F_e}} } \over q}

=

{{ - q{\upsilon _0}{B_0}\left( {14\widehat j + 7\widehat k} \right)} \over q}

=

-

\upsilon

₀ B₀ (14

{\widehat j}

+ 7

{\widehat k}

)

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