A charged particle of specific charge $α$ moves with a velocity $v = v_{0} \hat{i}$ in a magnetic field $B = \frac{B _{0}}{2} (\hat{j} + \hat{k})$ . Then : (specific charge $=$ charge per unit mass)

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Answer 1

1) Path of particle in magnetic field is either circular, straight line or helix, Here charged particle is projected at an angle so path must be circular.
2)
$\overline{v} = v_{0} \overline{i}$

$\overline{F} = q (\overline{v} \times \overline{B})$

$\overline{F} = q (v_{0} \overline{i} \times \frac{B}{2} (\overline{j} + \overline{k}))$

$\overline{F} = q v_{0} \frac{B}{2} (\overline{k} - \overline{j})$

Distance travelled by particle in time
$t = v \cdot t = v_{0} \cdot \frac{π}{B _{0} α}$

Answer 2

1) Path of particle in magnetic field is either circular, straight line or helix, Here charged particle is projected at an angle so path must be circular.
2)

\overline{v} = v_{0} \overline{i}

\overline{F} = q (\overline{v} \times \overline{B})

\overline{F} = q (v_{0} \overline{i} \times \frac{B}{2} (\overline{j} + \overline{k}))

\overline{F} = q v_{0} \frac{B}{2} (\overline{k} - \overline{j})

Distance travelled by particle in time

t = v \cdot t = v_{0} \cdot \frac{π}{B _{0} α}

A charged particle of specific charge $α$ moves with a velocity $v = v_{0} \hat{i}$ in a magnetic field $B = \frac{B _{0}}{2} (\hat{j} + \hat{k})$ . Then : (specific charge $=$ charge per unit mass)

path of the particle is a helix

path of the particle is a circle

distance moved by particle intime $t = \frac{π}{B _{0} α} i s \frac{π v _{0}}{B _{0} α}$

velocity of particle after time $t = \frac{π}{B _{0} α} i s (\frac{v _{0}}{2} \hat{i} + \frac{v _{0}}{2} \hat{j})$

A charged particle of unit mass and unit charge moves with velocity of $v = (8 \hat{i} + 6 \hat{j})$ m/s in a magnetic field of $B = 2 \hat{k} T$ . Then:

A proton is fired from origin with velocity $v = v_{0} j + v_{0} k$ in a uniform magnetic field $B = B_{0} j$ . In the subsequent motion of the proton:

A charged particle moves with a constant velocity $(\hat{i} + \hat{j}) m / s$ in a magnetic field $B = (2 \hat{i} + 3 \hat{k})$ and uniform electric field $E = (a \hat{i} + b \hat{j} + c \hat{k}) N / C$ , then $($ assuming all quantities in S.I. unit $) :$

A charged particle of specific charge $α$ moves with a velocity $v = v_{0} \hat{i}$ in a magnetic field $B = \frac{B _{0}}{2} (\hat{j} + \hat{k})$ . Then (specific charge $=$ charge per unit mass)

Revise with Concepts

Magnetic Field and Magnetic Force

A charged particle of specific charge α moves with a velocity v=v0​i^ in a magnetic field B=2​B0​​(j^​+k^). Then : (specific charge = charge per unit mass)

path of the particle is a helix

path of the particle is a circle

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velocity of particle after time t=B0​απ​is(2v0​​i^+2v0​​j^​)

A charged particle of unit mass and unit charge moves with velocity of v=(8i^+6j^​) m/s in a magnetic field of B=2k^T. Then:

A proton is fired from origin with velocity v=v0​j​+v0​k in a uniform magnetic field B=B0​j​. In the subsequent motion of the proton:

A charged particle moves with a constant velocity (i^+j^​)m/s in a magnetic field B=(2i^+3k^) and uniform electric field E=(ai^+bj^​+ck^)N/C , then (assuming all quantities in S.I. unit):

A charged particle of specific charge α moves with a velocity v=v0​i^ in a magnetic field B=2​B0​​(j^​+k^). Then (specific charge = charge per unit mass)

Revise with Concepts

Magnetic Field and Magnetic Force

A charged particle of specific charge $α$ moves with a velocity $v = v_{0} \hat{i}$ in a magnetic field $B = \frac{B _{0}}{2} (\hat{j} + \hat{k})$ . Then : (specific charge $=$ charge per unit mass)

distance moved by particle intime $t = \frac{π}{B _{0} α} i s \frac{π v _{0}}{B _{0} α}$

velocity of particle after time $t = \frac{π}{B _{0} α} i s (\frac{v _{0}}{2} \hat{i} + \frac{v _{0}}{2} \hat{j})$

A charged particle of unit mass and unit charge moves with velocity of $v = (8 \hat{i} + 6 \hat{j})$ m/s in a magnetic field of $B = 2 \hat{k} T$ . Then:

A proton is fired from origin with velocity $v = v_{0} j + v_{0} k$ in a uniform magnetic field $B = B_{0} j$ . In the subsequent motion of the proton:

A charged particle moves with a constant velocity $(\hat{i} + \hat{j}) m / s$ in a magnetic field $B = (2 \hat{i} + 3 \hat{k})$ and uniform electric field $E = (a \hat{i} + b \hat{j} + c \hat{k}) N / C$ , then $($ assuming all quantities in S.I. unit $) :$

A charged particle of specific charge $α$ moves with a velocity $v = v_{0} \hat{i}$ in a magnetic field $B = \frac{B _{0}}{2} (\hat{j} + \hat{k})$ . Then (specific charge $=$ charge per unit mass)