In a velocity selector, the electric and magnetic forces cancel if 𝐄+𝐯 ×𝐁=0 . Show that 𝐯 must b

Name: Problem 7, Chapter 19: College Physics
Uploaded: 2020-07-04T22:02:07-08:00
Duration: 1 min 24 s
Channel: Joseph Petrullo
Description: In a velocity selector, the electric and magnetic forces cancel if 𝐄+𝐯 ×𝐁=0 . Show that 𝐯 must be in the same direction as 𝐄 ×𝐁. [Hint: Since 𝐯 is perpendicular to both 𝐄 and 𝐁 in a velocity selector, there are only two possibilities for the direction of 𝐯 : the direction of 𝐄̂ ×𝐁 or the direction of -𝐄 ×𝐁 .]

step 1 So for this question, we can use the fact that F is equal to QV cross B. And so we know the dire

Question

In a velocity selector, the electric and magnetic forces cancel if $\overrightarrow{\mathbf{E}}+\overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{B}}=0 .$ Show that $\overrightarrow{\mathbf{v}}$ must be in the same direction as $\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$. [Hint: Since $\overrightarrow{\mathbf{v}}$ is perpendicular to both $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ in a velocity selector, there are only two possibilities for the direction of $\overrightarrow{\mathbf{v}}$ : the direction of $\hat{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$ or the direction of $-\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}} .]$

   In a velocity selector, the electric and magnetic forces cancel if $\overrightarrow{\mathbf{E}}+\overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{B}}=0 .$ Show that $\overrightarrow{\mathbf{v}}$ must be in the same direction as $\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$. [Hint: Since $\overrightarrow{\mathbf{v}}$ is perpendicular to both $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ in a velocity selector, there are only two possibilities for the direction of $\overrightarrow{\mathbf{v}}$ : the direction of $\hat{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$ or the direction of $-\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}} .]$

College Physics

lan Giambattista,… 2nd Edition

Chapter 19, Problem 7

Instant Answer

Solved by Expert Joseph Petrullo

07/04/2020

Step 1

Case 1: $\overrightarrow{\mathbf{v}}$ is in the direction of $\hat{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$. In this case, we can write $\overrightarrow{\mathbf{v}} = k(\hat{\mathbf{E}} \times \overrightarrow{\mathbf{B}})$, where $k$ is a scalar constant. Show more…

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In a velocity selector, the electric and magnetic forces cancel if $\overrightarrow{\mathbf{E}}+\overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{B}}=0 .$ Show that $\overrightarrow{\mathbf{v}}$ must be in the same direction as $\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$. [Hint: Since $\overrightarrow{\mathbf{v}}$ is perpendicular to both $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ in a velocity selector, there are only two possibilities for the direction of $\overrightarrow{\mathbf{v}}$ : the direction of $\hat{\mathbf{E}} \times \overrightarrow{\mathbf{B}}$ or the direction of $-\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}} .]$