Question

A proton experiences an eastward force of 30 × N while traveling in a magnetic field of 5 × T north. 

1. Find the magnitude of the proton’s velocity
2. State the direction of the proton’s velocity 
3. Draw the proton and indicate the directions of all three vectors using the appropriate notation as shown in the table above

Answer 1

To be given in question

Magnetic force =$30\hat{i}N$

Magnetic field= $5\hat{j}T$

To be asked in question

(a)Magnitude of proton velocity (v)=?

(b) velocity direction

(C) diagram

Part(a)

We know that

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

F=qvBsin$\theta$$(\hat{n})$

Magnitude of F

F=qvB $\rightarrow(1)$

$v=\frac{F}{qB}$

Put value

$v=\frac{30}{1.6\times10^{-19}\times5}$ m/sec

$v=3.75\times10^{19}m/sec$

Part {b}

State the direction of proton velocity

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

$F=qvBsin\theta\hat{n}$

$\hat{n}$ Direction$\overrightarrow({q}\times \overrightarrow{B} )direction$

F direction is $\hat{i}$ And

$(\overrightarrow{v}\times\overrightarrow {B})$

direction $\hat{i}$ Possible

When

Velocity V direction ($-\hat{k}$ )

Then we can written as

$\hat{i}=(-\hat{k}\times\hat{j})$

Which means velocity of proton move negetive z -axis

$V=-v\hat{k}$

Part(c)

According to diagram velocity direction is$-\hat{k}$