Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Question: A proton travels through uniform magnetic and electric fields. The magnetic field is $\vec{B} = - 2.5 \hat{i} mT$ .At one instant the velocity of the proton is $\vec{v} = 2000 \hat{j} m / s$ At that instant and in unit-vector notation, what is the net force acting on the proton if the electric field is (a) role="math" localid="1663233256112" $4.00 \hat{k} V / m$ , (b) $- 4.00 \hat{k} V / m$ and (c) $4.00 \hat{i} V / m$ ?

$\vec{F} = 1.44 \times 10^{- 18} \hat{k} N$
$\vec{F} = 1.60 \times 10^{- 19} \hat{k} N$
$\vec{F} = (6.41 \times 10^{- 19}) \hat{i} N + (8.01 \times 10^{- 19}) \hat{k} N$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

$\vec{B} = - 2.5 \hat{i} mT$

$\vec{v} = 2000 \hat{j} m / s$

Step 2: Determining the concept

The total force acting on the charged particle is the sum of the forces due to electric and magnetic fields.

Formulae are as follow:

Force acting on the charged particle due to electric field,

$F_{e} = q E$

Force acting on the charged particle due to magnetic field,

$F_{m} = q v B$

Where, $F_{m}$ is magnetic force, v is velocity, B is magnetic field, q is charge of particle.

Step 3: (a) Determining the net force acting on the proton if the electric field is 4.00k^ V/m

The net force on the proton when $\vec{E} = 4.00 \hat{k} V / m$ :

$\vec{F} = q (\vec{E} + \vec{V} \times \vec{B}) \vec{F} = 1.6 \times 10^{- 19} (4.00 \hat{k} + 2000 \hat{j} \times (- 2.5 \times 10^{- 3}) \hat{i}) \vec{F} = 1.6 \times 10^{- 19} (4.00 \hat{k} + 5.00 \hat{k}) \vec{F} = 1.44 \times 10^{- 18} \hat{k} N$

Hence, the net force acting on the proton is $\vec{F} = 1.44 \times 10^{- 18} \hat{k} N$

Step 4: (b) Determining the net force acting on the proton if the electric field is -4.00k^ V/m

Then net force on the proton when $\vec{E} = - 4.00 \hat{k} V / m$ :

$\vec{F} = q (\vec{E} + \vec{V} \times \vec{B}) \vec{F} = 1.6 \times 10^{- 19} (- 4.00 \hat{k} + 2000 \hat{j} \times (- 2.5 \times 10^{- 3}) \hat{i}) \vec{F} = 1.6 \times 10^{- 19} (- 4.00 \hat{k} + 5.00 \hat{k}) \vec{F} = 1.60 \times 10^{- 19} \hat{k} N$

Hence, the net force acting on the proton is $\vec{F} = 1.60 \times 10^{- 19} \hat{k} N$

Step 5: (c) Determining the net force acting on the proton if the electric field is-4.00i^ V/m

The net force on the proton when $\vec{E} = 4.00 \hat{i} V / m$

$\vec{F} = q (\vec{E} + \vec{V} \times \vec{B}) \vec{F} = 1.6 \times 10^{- 19} (4.00 \hat{i} + 2000 \hat{j} \times (- 2.5 \times 10^{- 3}) \hat{i}) \vec{F} = 1.6 \times 10^{- 19} (4.00 \hat{i} + 5.00 \hat{k}) \vec{F} = (6.41 \times 10^{- 19}) \hat{i} N + (8.01 \times 10^{- 19}) \hat{k} N$

Hence, the net force acting on the proton is $\vec{F} = (6.41 \times 10^{- 19}) \hat{i} N + (8.01 \times 10^{- 19}) \hat{k} N$ .

Therefore, the values of net force due to different electric fields can be determined by taking the vector sum of forces due to the electric and magnetic field.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the net force acting on the proton if the electric field is 4.00k^ V/m

Step 4: (b) Determining the net force acting on the proton if the electric field is -4.00k^ V/m

Step 5: (c) Determining the net force acting on the proton if the electric field is-4.00i^ V/m

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the net force acting on the proton if the electric field is 4.00k^ V/m

Step 4: (b) Determining the net force acting on the proton if the electric field is -4.00k^ V/m

Step 5: (c) Determining the net force acting on the proton if the electric field is-4.00i^ V/m

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