Question

The electric field in a region is uniform (constant in space) and given by E-( 148.0 1 -110.03)N/C. An additional charge 10.4 nC (nano-coulombs) is placed into this region. What is the y component of the electric force on this charge?

Answer 1

Answer:

$-1.144\ \mu C$

Explanation:

Given:

• $\vec{E}$ = uniform electric field in the space = $(148.0\ \hat{i}-110.0\ \hat{j})\ N/C$

• Q = Charge placed in the region = $10.4 nC\ = 1.04\times 10^{-8}\ nC$

Assume:

• $\vec{F}$ = Electric force on the charge due to electric field

We know that the electric field is the electric force applied on a unit positive charge i.e.,

$\vec{E}=\dfrac{\vec{F}}{Q}$

This means the electric force applied on this additional charge placed in the field is given by:

$\vec{F}=Q\vec{E}\\\Rightarrow \vec{F} = 1.04\times 10^{-8}\ n C\times (148.0\ \hat{i}-110.0\ \hat{j})\ N/C\\\Rightarrow \vec{F} = (1.539\ \hat{i}-1.144\ \hat{j})\ \mu N$

From the above expression of force, we have the following y-component of force on this additional charge.

$F_y = -1.144\ \mu N$

Hence, the y-component of the electric force on the this charge is $-1.144\ \mu N$.