So Im doing a hugepretest packet for my phys midterm coming up and I am just not

Question

So Im doing a hugepretest packet for my phys midterm coming up and I am just notunderstanding my physics book when it comes to line charges. Cansomeone please help me out?
Here's theQuestion: A non-uniform linecharge extends from –10 cm to +10 cm on thex-axis. The density has the form (x) = 0.02x^4. (a) What is the total chargeon the rod? (b) What is the electric field at the origin?(bothmagnitude and direction) So Im doing a hugepretest packet for my phys midterm coming up and I am just notunderstanding my physics book when it comes to line charges. Cansomeone please help me out?
Here's theQuestion: A non-uniform linecharge extends from –10 cm to +10 cm on thex-axis. The density has the form (x) = 0.02x^4. (a) What is the total chargeon the rod? (b) What is the electric field at the origin?(bothmagnitude and direction)

Explanation / Answer

Charge density = 0.02 x ^ 4 Charge q = integral dx   with in thelimits x = -10 to x = 10 cm                = integral 0.02x ^4   with in the limits x = -0.1 m tox=0.1 m                = 0.02 [ x ^ 5 ] / 5   with in the limits x= -0.1 mto x = 0.1 m               = 0.004 x ^ 5 with in the limirs x = -0.1 m tox-0.1 m               = 0.004 [ 0.1 ^ 5 - ( -0.1 ) ^ 5 ]               = 0.004 [ 0.00001 + 0.00001]               = 0.004 *0.00002               = 8 * 10 ^ -8 C

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