Question

Two charges, +7 µC and +13 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −5 nC charge when placed at the following locations. (a) halfway between the two magnitude N direction ---Select--- to the right to the left The magnitude is zero. (b) half a meter to the left of the +7 µC charge magnitude N direction ---Select--- to the right to the left The magnitude is zero. (c) half a meter above the +13 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.) magnitude N direction ° counterclockwise from the +x-axis

          Two charges, +7 µC and +13 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −5 nC charge when placed at the following locations. (a) halfway between the two magnitude N direction ---Select--- to the right to the left The magnitude is zero. (b) half a meter to the left of the +7 µC charge magnitude N direction ---Select--- to the right to the left The magnitude is zero. (c) half a meter above the +13 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.) magnitude N direction ° counterclockwise from the +x-axis

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Added by Melissa A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

01/20/2023

Step 1

We will use Coulomb's law, which states that the force between two point charges is given by: \[ F = k \frac{|q_1 q_2|}{r^2} \] where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), \( q_1 \) and \( q_2 \) are the magnitudes of Show more…

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Two charges, +7 µC and +13 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −5 nC charge when placed at the following locations. (a) halfway between the two magnitude N direction ---Select--- to the right to the left The magnitude is zero. (b) half a meter to the left of the +7 µC charge magnitude N direction ---Select--- to the right to the left The magnitude is zero. (c) half a meter above the +13 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.) magnitude N direction ° counterclockwise from the +x-axis

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Transcript

00:01 All right, so let's say we have two charges that are placed one meter apart.

00:06 Let's say q1 has a value of three microculems.

00:10 Q2 has a value of 12 microculems.

00:14 And we're placing a negative 2 nanoculum charge at various locations.

00:18 So the first case, it's halfway between the two.

00:20 We want to find the magnitude and direction of the net force between it.

00:24 So it's going to be k times q1 times, we'll just call it q.

00:31 So q is negative 2 nanofulms.

00:35 So k times q1 times q.

00:39 Now it's going to be pulled to the left.

00:40 So we'll put a negative sign.

00:44 Or better yet, let's not write it just yet.

00:46 So divided by this distance d over 2 squared.

00:50 And then this is plus q2 times q over d over 2 squared.

00:56 Now this one is in the opposite direction.

00:57 So actually we should have a negative sign here.

01:02 So that's what we'll have.

01:05 And so if we evaluate what that is, so it's q1 was 3 times 0 .9 times 3 times 10 to negative 6 divided by 0 .5 squared minus 12 times 10 to negative 6, divided by 0 .5 squared times 9 times 10 to the 9th times 2 times 10 to the negative 9th.

01:29 So this will be basically it'll be positive 6 .4a...

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