Chapter 4: Q27E (page 913)

Crossed E and B Fields. A particle with initial velocity $\vec{v} = (5.85 \times 10^{3} m / s) \hat{j}$ enters a region of uniform electric and magnetic fields. The magnetic field in the region is $\vec{B} = - (1.35 T) k$ . Calculate the magnitude and direction of the electric field in the region if the particle is to pass through undeflected, for a particle of charge (a) +0.640 nC and (b) -0.320 nC. You can ignore the weight of the particle.

Short Answer

Expert verified

a) The magnitude and direction of the charged particle of charge +0.640 nC is $(7898 N / C) \hat{i}$

b) The magnitude and direction of the charged particle of charge -0.320 nC is $(- 7898 N / C) \hat{i}$

Step by step solution

Magnetic force and electric force

The magnetic force on a particle is given by

$\vec{F_{B}} = q (\vec{v} \times \vec{B})$

Here q is the charge of the particle and v is the velocity of the particle

And the electric force is

$\vec{F_{E}} = q \vec{E}$

Determine the magnitude and direction of the first particle

(a)

The magnetic force is

$\vec{F_{B}} = q (\vec{v} \times \vec{B})$

And the electric force on the particle is

$\vec{F_{E}} = q \vec{E}$

Both forces are equal

Therefore,

$\begin{aligned} \vec{F_{E}} = \vec{F_{B}} \\ qvB = qE \\ E = vB \end{aligned}$

Put the values in the equation

$\begin{aligned} E = (5 .85 \times 10^{3} m / s) (1 .35 T) \\ = 7898 N / C \end{aligned}$

And the direction is $\hat{j} \times (- k) = - \hat{i}$

Therefore, the magnitude and direction of the charged particle of charge +0.640 nC is $(7898 N / C) \hat{i}$

Determine the direction and magnitude of the second particle

(b)

Same as the previous one,

The electric field of the second particle is

$\begin{aligned} \vec{E} = vB (- \hat{i}) \\ E = (5 .85 \times 10^{3} m / s) (1 .35 T) (- \hat{i}) \\ = - 7898 N / C \end{aligned}$

Therefore, the magnitude and direction of the charged particle of charge +0.640 nC is $(- 7898 N / C) \hat{i}$

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Short Answer

Step by step solution

Magnetic force and electric force

Determine the magnitude and direction of the first particle

Determine the direction and magnitude of the second particle

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