An electron is moving with a velocity 2 × 106 m/s along positive x-direction in the uniform electric field of 8 × 107 V/m applied along positive y-direction. The magnitude and direction of a uniform magnetic field (in Tesla) that will cause the electrons to move undeviated along its original path is

Question

An electron is moving with a velocity 2 × 106 m/s along positive x-direction in the uniform electric field of 8 × 107 V/m applied along positive y-direction. The magnitude and direction of a uniform magnetic field (in Tesla) that will cause the electrons to move undeviated along its original path is (A) 40 in -ve z-direction (B) 40 in +ve z-direction (C) 4 in +ve z-direction (D) 4 in -ve z-direction

Tardigrade Admin · Accepted Answer

For electrons to move undeviated along its original path,

\Rightarrow

Electric force

=

Magnetic force
or

qE = q v B

or

B = \frac{E}{v} = \frac{8 \times 1 0 ^{7}}{2 \times 1 0 ^{6}}

B = 40 T

Direction of magnetic field will be

-

ve

z

-direction because of negative charge.

Q. An electron is moving with a velocity 2×106m/s along positive x-direction in the uniform electric field of 8×107V/m applied along positive y-direction. The magnitude and direction of a uniform magnetic field (in Tesla) that will cause the electrons to move undeviated along its original path is

40 in -ve z-direction

40 in +ve z-direction

4 in +ve z-direction

4 in -ve z-direction

8 in +ve z-direction

For electrons to move undeviated along its original path, ⇒ Electric force = Magnetic force or qE=qvB or B=vE​=2×1068×107​ B=40T Direction of magnetic field will be − ve z -direction because of negative charge.

For electrons to move undeviated along its original path,
$\Rightarrow$ Electric force $=$ Magnetic force
or $qE = q v B$
or $B = \frac{E}{v} = \frac{8 \times 1 0 ^{7}}{2 \times 1 0 ^{6}}$
$B = 40 T$
Direction of magnetic field will be $-$ ve $z$ -direction because of negative charge.