A charged particle of unit mass and unit charge moves with velocity $v = (8 \hat{i} + 6 \hat{j}) m s^{- 1}$ in a magnetic field of $B = 2 \hat{k} T$ . Choose the correct alternative(s).

Question

Verified by Toppr

Answer 1

$v = 8 \hat{i} + 6 \hat{j}$
$B = 2 \hat{k}$
$m = 1$
$q = 1$
$r = \frac{m v}{q B} = \frac{1 \times 8 ^{2} + 6 ^{2}}{1 \times 2} = 5$

The trajectory will be circular and will be in xy plane.
a) $x^{2} + y^{2} - 4 x - 21 = 0$
$∴ (x - 2)^{2} + y^{2} - 4 - 21 = (x - 2)^{2} + y^{2} = 25 = 5^{2}$ which is equation of a circle of radius 5.
b) $x^{2} + y^{2} = 25$ is equation of circle of radius 5.
c) $y^{2} + z^{2} = 25$ gives the circle being in yz plane, which is not correct.
d) $T = \frac{2 π r}{v} = \frac{2 \times 3 . 1 4 \times 5}{1 0} = 3.14 m / s$

Answer 2

v = 8 \hat{i} + 6 \hat{j}

B = 2 \hat{k}

m = 1

q = 1

r = \frac{m v}{q B} = \frac{1 \times 8 ^{2} + 6 ^{2}}{1 \times 2} = 5

The trajectory will be circular and will be in xy plane.
a)

x^{2} + y^{2} - 4 x - 21 = 0

∴ (x - 2)^{2} + y^{2} - 4 - 21 = (x - 2)^{2} + y^{2} = 25 = 5^{2}

which is equation of a circle of radius 5.
b)

x^{2} + y^{2} = 25

is equation of circle of radius 5.
c)

y^{2} + z^{2} = 25

gives the circle being in yz plane, which is not correct.
d)

T = \frac{2 π r}{v} = \frac{2 \times 3 . 1 4 \times 5}{1 0} = 3.14 m / s