# Preliminary Past Paper Question (1 Viewer)

#### Ambility

##### Active Member
I was just doing a past paper and my answer to a question didn't match the answer in the answers. Here's the question.

A magician decides to use an electric field to levitate (float) a light plastic ball in the air. The ball has a mass of 15 grams and can be given a charge of +0.5 coulombs. Determine the strength and direction of the external electric field that the magician would require to levitate the ball.

I got $0.294 NC^{-1}$ where the answers say $29.4 NC^{-1}$.

Who's right?

#### InteGrand

##### Well-Known Member
I was just doing a past paper and my answer to a question didn't match the answer in the answers. Here's the question.

A magician decides to use an electric field to levitate (float) a light plastic ball in the air. The ball has a mass of 15 grams and can be given a charge of +0.5 coulombs. Determine the strength and direction of the external electric field that the magician would require to levitate the ball.

I got $0.294 NC^{-1}$ where the answers say $29.4 NC^{-1}$.

Who's right?
Since your answer and the given answers differ by some orders of magnitude, the error may be due to units: did you make sure to convert the mass of the ball to SI units of kg (i.e. use 0.015 as the value for m in any equations)?

Edit: just did the Q, and got 0.294 using 0.015 kg for mass. So the answers probably made the mistake with units somewhere (though they are out by two orders of magnitude; if they had used m = 15, they would have been out by three. Maybe they just used m = 1.5 or something).

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#### MilkyCat_

##### Active Member
Can you give some working out for this question as I remember I was stuck on a similar one
thanks

#### Crisium

##### Pew Pew
Can you give some working out for this question as I remember I was stuck on a similar one
thanks
Sure thing

Using the formula E = F / q

You know the value of q but not the value of E and F

Remember that F = mg and since they have given you the value of m (0.015 kg) and you know the value of g (9.8) you can find F and hence find E

F = 0.015 x 9.8

F = 0.147

Therefore

E = 0.147 / 0.5

E = 0.294 NC^-1

Remember to convert everything to the right units!

#### MilkyCat_

##### Active Member
Sure thing

Using the formula E = F / q

You know the value of q but not the value of E and F

Remember that F = mg and since they have given you the value of m (0.015 kg) and you know the value of g (9.8) you can find F and hence find E

F = 0.015 x 9.8

F = 0.147

Therefore

E = 0.147 / 0.5

E = 0.294 NC^-1

Remember to convert everything to the right units!
ah wow it was that easy haha
cheers man

#### InteGrand

##### Well-Known Member
Can you give some working out for this question as I remember I was stuck on a similar one
thanks
$The weight force of the ball has magnitude W=mg, where m=0.015\text{ kg} and g=9.8 \text{ m s}^{-2}.$

$The magnitude of the force of the electric field is F_E = Eq, where q=+0.5\text{ C} and E is the magnitude of the electric field. Since we require F_E=W for the ball to levitate (as the opposing forces must be equal in magnitude to cancel out and leave no acceleration), we require Eq=mg\Rightarrow E = \frac{mg}{q}=\frac{0.015\text{ kg}\times 9.8 \text{ m s}^{-2}}{0.5\text{ C}}=0.294\text{ N C}^{-1}. The direction of the field, which is defined as the direction a positive charge would experience a force, is going to be in the opposite direction to the gravitational force, i.e. up (since the charge given is positive). (Recall that electric field is a vector quantity so direction is important (and is asked for by the question).)$