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Points]

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SERPSE10 28.A.OP.027.MI. A particle with positive charge

`q=1.92\times 10^(-18)`

C moves with a velocity

`vec(v)=(5hat(i)+4hat(j)-hat(k))(m)/(s)`

thiuugh a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking

`vec(B)=(5hat(i)+2hat(j)+hat(k))T`

and

`vec(E)=(5hat(i)-hat(j)-4hat(k))(V)/(m)`

. (Give your answers in

`N`

for each component.)

```
F_(x)=
The force will be the sum of the force due to the electric field and the force due to the magnetic field. N
F_(y)=
What is the equation for the force exerted by a magnetic field on a moving charge? N
F_(Z)=
```

How does the magnetic force depend on the velocity of the charge?

`N`

(b) What angle does the force vector make with the positive

`x`

-axis?. (Give your answer in degrees counterclockwise from the

`+x`

-axis.)

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Note that the dot product of a vector with a unit vector

`hat(i)`

gives

`vec(V)*hat(i)=Vcos(\theta )`

where

`\theta `

is the angle between the two vectors.

`\deg `

counterclockwise from the

`+x`

-axis (c) What If? For what vector electric field would the total force on the particle be zero? (Give your answers in

`(V)/(m)`

for each component.)

```
E_(x)=,✓(V)/(m)
E_(y)=,\times (V)/(m)
E_(z)=,(V)/(m)
```