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Q12P

Expert-verifiedFound in: Page 829

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**At time t_{1}, an electron is sent along the positive direction of an x-axis, through both an electric field **

**(a)the magnitude E and **

**(b $\overrightarrow{\mathbf{B}}{\mathbf{}}$)****in unit-vector notation.**

a.$\text{E}=\text{1.25 V/m}$

b.$\stackrel{\rightharpoonup}{B}=0.\text{025 T}\stackrel{\wedge}{K}$

When,$v=0,$$F=-{\text{2\xd710}}^{\text{-19}}\text{N}$

**The direction of the magnetic force **

**Right Hand Rule states that if we arrange our thumb, forefinger, and middle finger of the right-hand perpendicular to each other, then the thumb points towards the direction of the motion of the conductor relative to the magnetic field, and the forefinger points towards the direction of the magnetic field and the middle finger points towards the direction of the induced current.**

Formulae are as follows:

role="math" localid="1663013317461" $\text{E}=\frac{\text{F}}{\text{q}}\phantom{\rule{0ex}{0ex}}=\text{q}(\stackrel{\rightharpoonup}{V}\times \stackrel{\rightharpoonup}{B})$

Where F is a magnetic force, v is velocity, E is the electric field, B is the magnetic field, and q is the charge of the particle.

To find the magnitude of E:

Here,

$\text{F}=\text{qE}\phantom{\rule{0ex}{0ex}}\begin{array}{c}E=\frac{F}{q}\\ =\frac{-2\times {10}^{-19}\text{\hspace{0.17em}}N}{-1.6\times {10}^{-19}\text{\hspace{0.17em}}C}\\ =1.25\text{\hspace{0.17em}}N/C\end{array}$

Hence, the magnitude of E is $1.25\text{\hspace{0.17em}}N/C$

To find a magnetic field $\left(\stackrel{\rightharpoonup}{B}\right)$:

$\begin{array}{c}B=\frac{E}{v}\\ =\frac{1.25\text{\hspace{0.17em}}N/C}{50\text{\hspace{0.17em}}m/s}\\ =0.025\text{\hspace{0.17em}}T\end{array}$

To find the direction of role="math" localid="1663013448881" $\stackrel{\rightharpoonup}{B}$,

$\stackrel{\rightharpoonup}{F}=\text{q}(\stackrel{\rightharpoonup}{V}\times \stackrel{\rightharpoonup}{B})$

The net force is directed in direction and velocity in $\text{+x}$ direction, so by applying the right-hand rule,$\stackrel{\rightharpoonup}{B}$ must be directed in $\text{+z}$ direction.

Hence,

role="math" localid="1663013638135" $\stackrel{\rightharpoonup}{B}=\text{0.025 T}\stackrel{\wedge}{K}$

Hence, the magnetic field is $\stackrel{\rightharpoonup}{B}=\text{0.025 T}\stackrel{\wedge}{K}$.

** **

Therefore, the magnitude of the electric field and magnetic field can be determined by using the respective formulae. The direction of the magnetic field can be found by using the right-hand rule.

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