A) What is the magnitude of the electric field, E at point P located at z=3.60 c

Question

A)What is the magnitude of the electric field, E at point P located at z=3.60 cm ?

B)Consider other locations along the positive z-axis. At what value of z does E have its maximum value?

C)What is the maximum value of E on the z-axis?

D)If z is much smaller than R then E is proportional to z. (You should verify this by taking the limit of your expression for E for z much smaller than R.) If you place an electron on the z-axis near the origin it experiences a force Fz=-kz, where k is a constant. Obtain a numerical value for k.

A uniform circular ring of charge Q=6.10microCoulombs and radius R=1.30cm is located in the x-y plane, centered on the origin as shown in the figure. What is the magnitude of the electric field, E at point P located at z=3.60 cm ? Consider other locations along the positive z-axis. At what value of z does E have its maximum value? What is the maximum value of E on the z-axis? If z is much smaller than R then E is proportional to z. (You should verify this by taking the limit of your expression for E for z much smaller than R.) If you place an electron on the z-axis near the origin it experiences a force Fz=-kz, where k is a constant. Obtain a numerical value for k.

Explanation / Answer

a) magnitude of the electric field, E at point P located at z=3.60 cm

= kQz / sqrt(z^2 + R^2)^3

= (9 * 10^9 * 6.10 * 10-6 *3.60 * 10-2 ) / [sqrt((3.60cm^2 + 1.30cm ^2))^3]

= 3.52 * 10^7 N/C

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b) z = R/sqtr(2)

= (1.30 cm) / (sqrt 2)

= 9.19 * 10-3 m

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c) z = 9.19 * 10-3 m

kQz / sqrt(z^2 + R^2)^3

= (9 * 10^9 * 6.10 * 10-6 * 9.19 * 10-3 ) / [sqrt((9.19*10-3 ^2 + 1.30cm ^2))^3]

=1.25 * 10^8 N/C

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d) K = eKQ / R^3

e = 1.6x10 -19

k = (1.6 * 10-19 * 9* 10^9 * 6.10 * 10-6) / (1.30cm)^3

= 3.99 * 10-9 N/m

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